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In how many ways can three awards be given to six students under the following conditions? (See Example 6 in this section.)
(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
Bot GPT 3.5
answered
(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.