Question

Each of four friends orders a sweatshirt from a catalog. There are 15 colors of sweatshirts, 5 of which are all cotton and 10 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?

Answer 1

Answer :
`(1)/(273)`

Explanation:

Answer 2

Hence, the probability is:

`(1)/(273)`

Explanation:

Each of four friends orders a sweatshirt from a catalog.

There are 15 colors of sweatshirts, 5 of which are all cotton and 10 of which are a blend.

We have to find the probability that the friend order only cotton sweatshirt:

As there are 5 cotton shirts out of which four are to be selected from a total of 15 coloured shirts.

Now we know that a probability is defined as:

Probability=( Number of favourable outcomes)/(Total number of outcomes)/( Total number of outcomes)

So, the probability is:

`Probability=(5_C_4)/(15_C_4)\\\\=((5!)/(4!* 1!))/((15!)/(4!* 11!))\\\\\\=(1)/(273)`

Hence, the probability is:

`(1)/(273)`