Question

Find the number of permutations of the first 9 letters of the alphabet taking 6 letters at a time.

1034

60,480

54,320

84

Answer 1

Option 4 - 84

Explanation:

Given : Permutations of the first 9 letters of the alphabet taking 6 letters at a time.

To find : The number of permutation?

Solution :

According to question we apply combination to find the number of permutations of the first 9 letters of the alphabet taking 6 letters at a time as order doesn't matter.

The combination is given by,

`^nC_r=(n!)/(r!(n-r)!)`

Here, n=9 and r=6

`^9C_6=(9!)/(6!(9-6)!)`

`^9C_6=(9* 8* 7* 6!)/(6!* 3!)`

`^9C_6=(9* 8* 7)/(3* 2* 1)`

`^9C_6=3* 4* 7`

`^9C_6=84`

Therefore, The number of permutations of the first 9 letters of the alphabet taking 6 letters at a time is 84.

So, Option 4 is correct.

Answer 2

9P6 = 60,480

_____
= 9!/(9-6)!