Let n be the number of ways in which 5 men and 7 women can stand in a queue such that all the women stand consecutively. Let me be the number of ways in which the same 12 persons can stand in a queue such that exactly 6 women stand consecutively. Then the value of m n is
Answers
Answer with explanation:
It is given that, n is the number of ways in which 5 men and 7 women can stand in a queue .
So,either 5 men will come first and 7 women will come after or 7 Women will come first and 5 men will come after.
Total possible ways(n) =5!×7!+7!×5!
=2 ×5!×7!
=2×120×5040
=240 × 5040
=1209600
"m" be the number of ways in which the same 12 persons can stand in a queue such that exactly 6 women stand consecutively.
Possible number of ways(m)
either 6 men will come first and then 6 women will come after or 6 Women will come first and then 6 men will come after.
m=6!×6!+ 6!×6!
=2×6!×6!
=2×720×720
=1440×720
= 1036800
m n=1209600× 1036800
=1254113280000