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