A cat has a litter of six kittens. You plan to adopt 2 of the kittens. In how many ways can you choose 2 of the kittens from the litter?
There are 6 kittens when you're deciding which one you want to pick, so there are 6 ways of chosing one. Then, the number of kittens lowers to 5, so there are 5 ways of picking another. At all, there are 30 ways of chosing 2 kittens out of 6.
There are 15 ways to choose 2 of the kittens from the litter
The given parameters are:
The number of ways to select the 2 kittens is:
Ways = \(^nC_r\)
This gives
Ways = \(^6C_2\)
The combination formula is:
\(^nC_r = \frac{n!}{(n - r)!r!}\)
So, we have:
\(^6C_2 = \frac{6!}{(6 - 2)!2!}\)
Evaluate the difference
\(^6C_2 = \frac{6!}{4!2!}\)
Expand
\(^6C_2 = \frac{6 * 5 * 4!}{4! * 2 * 1}\)
Evaluate the quotient
\(^6C_2 = 15\)
So, we have:
Ways = 15
Hence, there are 15 ways to choose 2 of the kittens from the litter
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