Question

When you divide the number of permutations of 11 objects taken 3 at a time by​ 3!, you will get the number of combinations of 11 objects taken 3 at a time.

Answer 1

Answer:

Yes

Step-by-step explanation:

Permutation :

nPr = n! ÷ (n - r)!

nCr = n! ÷ (n-r)!r!

11 objects taken 3 at a time :

11P3 = 11! ÷ (11 - 3)!

11P3 = 11! / 8!

11P3 = (11 * 10 * 9 )

11P3 = 990

Dividing by 3!

3! = 3*2*1 = 6

= 990 / 6

= 165

For combination :

11C3 = 11! ÷ 8!3!

11C3 = (11 * 10 * 9) / (3 * 2 * 1)

11C3 = 990 / 6

11C3