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Question

The probability of obtaining exactly $$r$$ heads and $$\left ( n-r \right )$$ tails, when we toss $$n$$ unbiased coins is


A
rn
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B
(nr)n
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C
Cnr2n
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D
Cnr3n
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Solution

The correct option is D $$\dfrac{C_{r}^{n}}{2^{n}}$$
When we toss $$n$$ unbiased coins; selection of exactly $$r$$ heads from $$n$$ coins $$=C^{n}_{r}$$; (remaining coins will obtain $$(n-r)$$ tails)
Total number of ways which we could get by arranging $$n$$ number of coins is $$=2^{n}$$
Probability of obtaining exactly $$r$$ heads and $$(n-r)$$ tails is $$=\dfrac{C^{n}_{r}}{2^{n}}$$

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