There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is ___________.
Answer (integer)
1120
Solution
<p>Number of ways when B<sub>1</sub> and B<sub>2</sub> are not together</p>
<p>= Total number of ways of selecting 3 boys $-$ B<sub>1</sub> and B<sub>2</sub> are together</p>
<p>= <sup>10</sup>C<sub>3</sub> $-$ <sup>8</sup>C<sub>1</sub></p>
<p>= ${{10\,.\,9\,.\,8} \over {1\,.\,2\,.\,3}} - 8$</p>
<p>= 112</p>
<p>Number of ways to select 3 girls = <sup>5</sup>C<sub>3</sub> = 10</p>
<p>$\therefore$ Total number of ways = 112 $\times$ 10 = 1120</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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