In how many ways can three awards be given to six students under the following conditions? (See Example 6 in this section.)

Question

(a)
if each student may receive more than one award
ways
(b)
if each student may receive no more than one award
ways

show your work

Answer 1

(a) If each student may receive more than one award, the number of ways the three awards can be given to the six students is 6^3 = 216 ways.

(b) If each student may receive no more than one award, the number of ways the three awards can be given to the six students is 6P3 = 120 ways.

We can calculate this using the permutation formula nPr = n! / (n-r)!

6P3 = 6! / (6-3)! = 6! / 3! = 720 / 6 = 120

Therefore, there are 120 ways to give three awards to six students if each student may receive no more than one award.