Question

In a picnic with 20 persons where 6 chocolates will be given to the top 8 children(the chocolates are distinct: first, second). How many ways can this be done?

(a) ^18C6

(b) ^20P6

(c) ^25C4 * 6!

(d) ^19P5

I have been asked this question in a job interview.

The above asked question is from Counting topic in division Counting of Discrete Mathematics

Answer 1

Right answer is (b) ^20P6

To elaborate: This is a permutation problem since the chocolates are distinct. The answer is P(20, 6) -> the number of ways to arrange 20 things taken 6 at a time -> which is \(\frac{20!}{(20-6)!}\) = 20*19*18*17*16*15.