Question

In a college a committee of 7 people has to be selected from a group of 8 fourth year and 6 third year students. In how many ways can this committee be selected if in the committee, majority of fourth year students is required?

- 2320
- 2216
- 2416
- 1960

Solution

The correct option is **C** 2416

Majority of fourth year means out of 7, minimum 4 should be from fourth year.

Considering different possibilities:

No.from 4th yearWays of choosing 4th yearNo.from 3rd yearWays of choosing 3rd yearwys of choosing commitee48C4=7036C3=2070 ×20 =140058C5=5626C2=1556 ×15 =84068C6=2816C1=628 ×6 =16878C7=806C0=18 ×1=8Total2416

So, total no. of ways = 2416.

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