1.

A team of 6 is to be formed from a class consists of 5 boys and 4 girls, such that at least 2 boys and 3 girls should be in the team. How many ways that can be done?1. 302. 503. 754. 45

Answer» Correct Answer - Option 2 : 50

Concept:

  • The ways of arranging n different things = n!
  • The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\)
  • The no. of ways of arranging the n arranged thing and m arranged things together = n! × m!
  • The number of ways for selecting r from a group of n (n > r) = nCr 

Calculation:

Selection of 2 boys out of 5 = 5C2 = 10

Selection of 3 boys out of 5 = 5C3 = 10

Selection of 3 girls out of 4 = 4C3 = 4

Selection of 4 girls out of 4 = 4C4 = 1

Now the selection can be done in the ways = 2 boys and 4 girls + 3 boys and 3 girls

Hence number ways N = 5C2 × 4C4 + 5C3 × 4C3 

Total number of ways = 10 × 1 + 10 × 4 = 50 ways



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