A person wants to buy one fountain pen, one ball pen, and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?

Question

Philoid · Accepted Answer

Given: 10 fountain pens, 12 ball pens, and 5 pencil

We have to select one fountain pen from 10 fountain pens, one ball pen from 12 ball pens and one pencil from 5 pencils.

Therefore, the number of ways to select one fountain pen is ¹⁰C₁ and similarly the number of ways to select one ball pen is ¹²C₁ and number of ways to select one pencil from 5 pencils in ⁵C₁

Hence, the number of ways to select one fountain pen, one ball pen and one pencil from a stationery shop is ¹⁰C₁ × ¹²C₁ × ⁵C_{1 =} 10 × 12 × 5 = 600