Question

Out of first $20$ natural numbers, $3$ numbers are selected such that there is exactly one even number.How many different selections can be made ?

Answer 1

There are total 10 even number in first 20 natural number.
Selecting one even number is ${=}^{10}{C}_1=10$
and selecting two odd number out of remaining 10 odd numbers is ${=}^{10}{C}_2=45$
So, No. of ways to select 3 numbers such that there is exactly one even number ${=}^{10}{C}_1{\times }^{10}{C}_2=10\times 45=450$