Question

You own 6 hats and are taking 2 on vacation. In how many different ways can you choose 2 hats from 6

Answer 1

Answer: 15 ways.

Step-by-step explanation:

Total number of hats owned =6

The number of hats taking on vacation=2

To find the different ways to choose 2 hats from 6, we use combination with n=6 and r=2, we get

The number of ways to choose 2 hats from 6=$^nC_r=^6C_2$

$=\frac{6!}{(6-2)!2!}\\\\=\frac{6\times5\times4!}{4!\times2!}\\\\=\frac{6\times5}{2}\\\\=3\times5=15\ \text{ways}$

Hence, in 15 ways we can choose 2 hats from 6 hats.

Answer 2

Hats 1,2,3,4,5,6
1,2
1,3
1,4
1,5
1,6
2.3
2,4
2,5
2,6
3,4
3,5
3,6
4,5
4,6
5,6

15 different combinations