Question

A coin is tossed 8 times. In how many ways can we obtain at least 6 heads?

Answer 1

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