A coin whose faces marked 2 and 3 is thrown 5 times, then chance of obtaining a

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A coin whose faces marked 2 and 3 is thrown 5 times, then chance of obtaining a total of 12 is

Options:

A . 516

B . 58

C . 532

D . 524

Answer: Option A
:
A
It is given that the coin has faces 2 and 3, tossed five times.
To get sum 12 we need 2,2,2,3,3 in any combination.
So, in the 5 throws, there need to be 3 2's. Automatically other 2 will be 3's since there is no other possibility.
So, it boils down to choosing 3 from 5.
Therefore P(getting sum 12)

= 5 C_{3} {(\frac{1}{2})}^{5} = \frac{5}{16} .

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