Class 11

Math

JEE Main Questions

Permutations and Combinations

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

(i) exactly 3 girls ?

(ii) atleast 3 girls ?

(iii) atmost 3 girls ?

total ways = $._{4}C_{3}._{9}C_{4}$

$=4⋅4⋅3⋅29⋅8⋅7⋅6 =63⋅8$

$=504$

(ii) $g=3or4$

total ways =$._{4}C_{3}._{9}C_{4}+._{4}C_{4}._{9}C_{3}$

$4⋅5⋅4⋅3⋅29⋅8⋅7⋅6⋅5 +3⋅29⋅8⋅7 $

$=504+84$

$=588$

(iii)$g=1,2,3$

total ways $=._{13}C_{7}−._{4}C_{4}._{9}C_{3}$

$=6⋅3⋅2⋅5⋅413⋅12⋅11⋅10⋅9⋅8 −84$

$=143⋅12−84$

$=1716−84$

answer