﻿ How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent? | Permutations and Combinations

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# Permutations and Combinations

#### Multiple Choice Questions

1.

The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is

• 216

• 192

• 120

• 120

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2.

If m is the AMN of two distinct real numbers l and n (l,n>1) and G1, G2, and G3 are three geometric means between l and n, then  equals

• 4l2 mn

• 4lm2n

• 4 lmn2

• 4 lmn2

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# 3.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent? 8 . 6C4 . 7C4 6 . 7 . 8C4 6 . 8 . 7C4 6 . 8 . 7C4

D.

6 . 8 . 7C4

Other than S, seven letters M, I, I, I, P, P, I can be arranged in 7!/2! 4!=7 . 5 . 3.

Now four S can be placed in 8 spaces in 8 C4 ways. Desired number of ways = 7 . 5 . 3 . 8C4 = 7 . 6C4 . 8C4.

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4.

The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-

• 12!/3!(4!)3

• 12!/3!(3!)4

• 12!/(4!)3

• 12!/(4!)3

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5.

The value  of

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6.

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

• 120

• 480

• 360

• 360

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7.

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

• 5

• 8C3
• 38

• 38

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8.

The number of all numbers having 5 digits, with distinct digits is

• 99999

• ${}^{10}\mathrm{P}_{5}$

• ${}^{9}\mathrm{P}_{4}$

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9.

The greatest integer which divides (p + 1) (p + 2) (p + 3) .... (p + q) for all p E N and fixed q $\in$ N is

• p!

• q!

• p

• q

10.

The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is

• $\frac{7!}{2!}$

• $\frac{6!}{2!}$

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