Question

In how many ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes

Answer 1

3 students should share one prize then it could be possible for you to distribute the prizes

Answer 2

Answer:

220 ways

Step-by-step explanation:

Total number of students = 12

No. of prizes = 3

Now we are supposed to find In how many ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes.

So, We will use combination over here

Formula : $^nC_r=\frac{n!}{r!(n-r)!}$

No. of ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes = $^{12}C_3$

No. of ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes = $\frac{12!}{3!(12-3)!}$

                                             = $220$                    

Hence there are 220 ways 3 prizes can be given away to 12 students when each student is eligible for all the prizes