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Find the number of ways in which 5 boys and 3 girls can be arranged in a row so that no two girls are together. |
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Answer» In order that no two girls are together , we must arrange the 5 boys, each denoted by B, as under: X B X B X B X B X B X Here, B denotes the position of a boy and X that of a girl. Number of ways in which 5 boys can be arranged at 5 places `=""^(5)P_(5)=5! =(5xx4xx3xx2xx1)=120.` Number of ways in which 3 girls can be arranged at 6 places (each marked X) `=""^(6)P_(3)=(6xx5xx4)=120.` Hence, by the fundamental principle of multiplication, the required number of ways `=(120xx120)=14400. |
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