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प्रश्न
A coin is tossed 8 times. In how many ways can we obtain at least 6 heads?
बेरीज
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उत्तर
A coin is tossed 8 times.
So the number of possible trials is n = 8.
Outcomes are head or tail.
At least 6 heads mean either 6 heads and 2 tails or 7 heads and 1 tail or 8 heads and 0 tail,
i.e., p = 6, q = 2 or p = 7, q = 1 or p = 8, q = 0
∴ the number of ways in which we can obtain at least 6 heads is
`("n"!)/("p"!"q"!) + ("n"!)/("p"!"q"!) + ("n"!)/("p"!"q"!)`
= `(8!)/(6!2!) + (8!)/(7!1!) + (8!)/(8!0!)`
= `(8 xx 7 xx 6!)/(6! xx 2 xx 1) + (8 xx 7!)/(7! xx 1) + (8!)/(8! xx 1)`
= 28 + 8 + 1
= 37
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