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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 can 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. In a stage show, f(4) superstars and f(3) junior artists participate. each one is going to present one item, then the number of ways the sequence of items can be planned, if no two junior artists present their items consecutively, 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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