Permutations and Combinations

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

• 96

• 144

• 512

• 576

If ${}^{\mathrm{n} - 1}\mathrm{C}_{3 }+ {}^{\mathrm{n} - 1}\mathrm{C}_4 > {}^{\mathrm{n}}\mathrm{C}_3$ then n is just greater than integer

• 5

• 6

• 4

• 7

Product of any r consecutive natural numbers is always divisible by

• r!

• (r + 4)!

• (r + 1)!

• (r + 2)!

A polygon has 44 diagonals. The number of its sides is

• 10

• 11

• 12

• 13

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points ?

• 26

• 28

• 27

• 25

How many odd numbers of six significant digits can be formed with the digits 0, 1, 2, 5, 6, 7 when no digit is repeated ?

• 120

• 96

• 360

• 288

The number of ways four boys can be seated around a round-table in four chairs of different colours is

• 24

• 12

• 23

• 64

If ${}^{16}\mathrm{C}_{\mathrm{r}} = {}^{16}\mathrm{C}_{\mathrm{r} + 1}$, then the value of ${}^{\mathrm{r}}\mathrm{P}_{\mathrm{r} - 3}$ is

• 31

• 12

• 210

• None

20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

• 20!

• 2(18!)

• 18!

• None of these

There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

• 119

• 44

• 59

• 40