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ક્રમચય અને સંચય

mn ભિન્ન વસ્તુઓનું n સમાન ભાગમાં ........ રીતે વિભાજન કરી શકાય.

$fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction bold cross times bold space fraction numerator bold 1 over denominator bold n bold space bold factorial end fraction$
$fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction$
$fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction bold cross times bold 1 over bold n$
આપેલ પૈકી એક પણ નહી

open parentheses table row bold 43 row bold 4 end table close parentheses bold space bold plus bold space bold sum from bold r bold equals bold 1 to bold 5 of bold space open parentheses table row cell bold 48 bold minus bold r end cell row bold 3 end table close parentheses bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space

$open parentheses table row bold 48 row bold 4 end table close parentheses$
$open parentheses table row bold 47 row bold 4 end table close parentheses$
$open parentheses table row bold 48 row 5 end table close parentheses$
$open parentheses table row bold 48 row bold 3 end table close parentheses$

open parentheses table row bold 48 row bold 4 end table close parentheses

Tips: -

$open parentheses table row bold 43 row bold 4 end table close parentheses bold space bold plus bold space bold sum from bold r bold equals bold 1 to bold 5 of bold space open parentheses table row cell bold 48 bold minus bold r end cell row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 43 row bold 4 end table close parentheses bold space bold plus bold space open parentheses table row bold 47 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 46 row bold 3 end table close parentheses bold space bold plus open parentheses table row bold 45 row bold 3 end table close parentheses bold plus bold space open parentheses table row bold 44 row bold 3 end table close parentheses bold space bold plus open parentheses table row bold 43 row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 43 row bold 4 end table close parentheses bold plus open parentheses table row bold 43 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 44 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 45 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 46 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 47 row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 44 row bold 4 end table close parentheses bold space bold plus bold space open parentheses table row bold 44 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 45 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 46 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 47 row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 45 row bold 4 end table close parentheses bold space bold plus bold space open parentheses table row bold 45 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 46 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 47 row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 46 row bold 4 end table close parentheses bold space bold plus bold space open parentheses table row bold 46 row bold 3 end table close parentheses bold space bold plus bold space open parentheses table row bold 47 row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 47 row bold 4 end table close parentheses bold space bold plus bold space open parentheses table row bold 47 row bold 3 end table close parentheses bold equals bold space open parentheses table row bold 48 row bold 4 end table close parentheses$

કુલ m + n + p વસ્તુઓનું m, વસ્તુઓ, n વસ્તુઓ અને p વસ્તુઓના ત્રણ ભાગમાં વિભાજન કેટલી રીતે કરી શકાય ?

$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p end fraction bold cross times bold space bold 3$
$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p end fraction bold cross times bold space bold 1 over bold 6$
$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p end fraction bold cross times bold space bold 3 bold space bold factorial$
$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction$

જો $bold m bold space bold equals bold space bold sum from bold r bold equals bold 0 to bold 100 of bold space fraction numerator bold 1 over denominator open parentheses table row bold 100 row bold r end table close parentheses end fraction bold comma$ તો $bold sum from bold r bold equals bold 0 to bold 100 of bold space fraction numerator bold r over denominator open parentheses table row bold 100 row bold r end table close parentheses end fraction bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space$

100 m
200 m
50 m
99 m

m + n + p વસ્તુઓમાંથી m, n અને p વસ્તુઓને ત્રણ ખાનામાં કુલ ........ રીતે મૂકી શકાય ?

$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction bold space bold cross times bold space bold 3$
$fraction numerator bold left parenthesis bold m bold space bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction bold space bold cross times bold space bold 1 over bold 6$
$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction$
$fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction bold space bold cross times bold space bold 3 bold space bold factorial$

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