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Let f(n) denotes the number of different...

Let f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5.
i.e., `4=1+1+1+1`
`=1+1+2=1+2+1=2+1+1=2+2`
Q. The number of solutions of the equation `f(n)=n`, where `n in N` is

A

144

B

360

C

4320

D

14400

Text Solution

Verified by Experts

The correct Answer is:
D
Number of superstars`=f(4)=5`
and number of junior artist `=f(3)=3`
`xxS_(1)xxS_(2)xxS_(3)xxS_(4)xxS_(5)xx` [`S_(i)` for superstars]
`therefore`Required number of ways`=.^(6)C_(3)xx5!xx3!=14400`.
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