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Question: Answered & Verified by Expert
In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together
MathematicsPermutation CombinationJEE Main
Options:
  • A $5!\times 3!$
  • B ${ }^4 P_3 \times 5!$
  • C ${ }^6 P_3 \times 5!$
  • D ${ }^5 P_3 \times 3!$
Solution:
1519 Upvotes Verified Answer
The correct answer is: ${ }^6 P_3 \times 5!$
Since the 5 boys can sit in 5 ! ways. In this case there are 6 places are vacant in which the girls can sit in ${}^{6} P_3$ ways. Therefore required number of ways are ${}^{6} P_{3} * 5$ !.

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