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JEE Main 20199 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
9 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2019 · 9 April · Morning Shift · Mathematics · Permutation and Combination

A committee of 11 member is to be formed from 8 males and 5...

A committee of 1111 member is to be formed from 88 males and 55 females. If mm is the number of ways the committee is formed with at least 66 males and nn is the number of ways the committee is formed with at least 33 females, then:

Options

  1. Am=n=68m = n = 68
  2. Bn=m–8n = m – 8
  3. Cm=n=78m = n = 78
  4. Dm+n=68m + n = 68

Correct answer

C. m=n=78m = n = 78

Step-by-step solution

m=(6M,5F)+(7M,4F)+(8M,3F)m = ( 6M, 5F ) + ( 7M, 4F ) + ( 8M, 3F )

=C68×C55+C78×C45+C88×C35= {C}_{6} 8 \times {C}_{5} 5 + {C}_{7} 8 \times {C}_{4} 5 + {C}_{8} 8 \times {C}_{3} 5

=28×1+8×5+1×10=78= 28 \times 1 + 8 \times 5 + 1 \times 10 = 78

n=(3F,8M)+(4F,7M)+(5F,6M)n = ( 3F, 8M ) + ( 4F, 7M ) + ( 5F, 6M )

=C35×C88+C45×C78+C55×C68= {C}_{3} 5 \times {C}_{8} 8 + {C}_{4} 5 \times {C}_{7} 8 + {C}_{5} 5 \times {C}_{6} 8

=10×1+5×8+1×28=78= 10 \times 1 + 5 \times 8 + 1 \times 28 = 78

Hence, m=n=78.m = n = 78 .

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