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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?
  1. 2320
  2. 2216
  3. 2416
  4. 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=1×1=8Total2416

So, total no. of ways = 2416. 

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