We have seven different pairs of shoes and eight different p

We have seven different pairs of shoes, and eight different pairs of socks.

(a) How many ways are there to pick a pair of shoes and a pair of socks?

(b) How many ways are there to pick a pair of shoes and two socks, not necessarily from the same pair? (Socks in the same pair are identical, but socks from different pairs are different.)

Solution

(a) We can pick a pair of shoes in ⁷C₁=7 ways

We can pick a pair of socks in ⁸C₁=8 ways

So no of ways are there to pick a pair of shoes and a pair of socks=7*8=56

B.)We can pick a pair of shoes in ⁷C₁=7 ways

We can pick a pair of socks , not necessarily of same time in ^2+5-1C₂ ways=15

Reason: Formula:

If we are selecting an r-combination from n types of elements with repetition, there are C(n+r1,r)=C(n+r1,n1) ways to do so.

So ways are there to pick a pair of shoes and two socks, not necessarily from the same pair=15*7=105