The are 6 girls and 5 boys standing in a queue. Amit is one of the boys and he always stands at the end of the queue. No two boys stand in consecutive positions. How many arrangements are possible?

Question

Answer 1

first arrange the girls =6!
there will be 7 positions for boys.
consider amir at 1st position. so remaining boys in 6 posittions=6p4
now consider amir at last. so for remaining boys arrangement=6p4
so it will be 6!.2.6p4

Answer 2

first arrange the girls =6!
there will be 7 positions for boys.
consider amir at 1st position. so remaining boys in 6 posittions=6p4
now consider amir at last. so for remaining boys arrangement=6p4
so it will be 6!.2.6p4

Answer 3

6*5!*6p4

Answer 4

6*5!*6p4

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The are 6 girls and 5 boys standing in a queue. Amit is one of the boys and he always stands at the end of the queue. No two boys stand in consecutive positions. How many arrangements are possible?