PERMUTATION AND COMBINATION
Probability
Level
3
Find the number of ways of permuting the numbers 1,2,3,....n so that they are first increasing and then decreasing.
2^(n-1)-4
2^n-1
2^(n-1)-2
2^(n-2)-1
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1 solution
Let assume 1,2,3,4,5 now keeping 5 in the middle both side should have 12534. Now keep n in the middle we are left with n-1 numbers which are distributed in two groups one to the left of n and to the right of n. so the group size can b like this 1 and n-1 or 2 and n-2 or 3 and n-3....so on which can be done in (n-1)C1+(n-1)C2+(n-1)C3+....+n-1Cn-2=2^(n-1)-2.