Question

How many different ways could a baking contest be judged if 15 pies are entered and 4 ribbons are awarded?

Answer 1

This is a question of combination since it does not take into account the order of the pies. The answer would be 1365. There are 1365 ways a baking contest ways can be judged if 4 ribbons are awarded with 15 pie entries. 

In case you need the order, then the permutation answer would be 32760.

Answer 2

Answer:

1365

Step-by-step explanation:

We are given that 15 pies are entered in the contest.

Out of 15 , 4 are awarded with ribbons.

Now we are supposed to find How many different ways could a baking contest be judged.

Since the order of pie doesn't matter over here.

So, we will use combination.

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

Substitute n = 15

r = 4

So, $^{15}C_4=\frac{15!}{4!(15-4)!}$

$^{15}C_4=\frac{15!}{4!(11)!}$

$^{15}C_4=\frac{15 \times 14\times 13 \times 12 \times 11!}{4!(11)!}$

$^{15}C_4=\frac{15\times 14\times 13 \times 12}{4\times 3 \times 2\times 1}$

$^{15}C_4=1365$

Hence there are 1365 ways in which a baking contest could be judged.