Question

I want to take a picture of my six friends standing in two horizontal rows of three. How many different photos can I take if the tallest person must stand in the back row, the shortest person must stand in the front row, and two of my friends are identical twins whom I can't tell apart? (The identical twins are neither the tallest nor the shortest.)

Answer 1

108 Ways

Explanation:

I did this on AoPs :)

Answer 2

Answer:108 ways

Explanation:

It is given that there 6 students with Tallest, shortest and 4 medium sized student

back row can be filled with Tallest person and 2 other from 4 medium sized student (shortest must be in front row)

No of ways in which 2 seats can be filled is
`4* 3`

and tallest can take any position out of 3 seats so total no of ways in which last row can be filled is
`=3* 4* 3=36\ ways`

In front row 3 students can be arranged in 3! ways i.e.
`6\ ways`

so total ways are
`6* 36=216\ ways`

but there are 2 twin which cut the total no of ways to half so total no of ways
`=(216)/(2)=108\ ways`