A coin is tossed 7 times. In how many different ways can we obtain
(a) 4 heads and 3 tails?
(b) at least 5 heads?
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⁷C₄
Answer:
Step-by-step explanation:
A coin is tossed 7 times. In how many different ways can we obtain
(a) 4 heads and 3 tails?
(b) at least 5 heads?
total number of possible outcomes = 2⁷ = 128
number of ways of 4 heads = ⁷C₄ = 7!/(4!3!) = (7 * 6 * 5) / (3 * 2) = 35
If 4 heads are there then automatically there will be 3 Tails
we can obtain 4 heads & 3 Tails in 35 Ways
Probability of 4 heads & 3 Tails = 35/128 = 0.27
Atleast 5 Heads means
5 Heads or 6 heads or 7 Heads
= ⁷C₅ + ⁷C₆ + ⁷C₇
= 7!/5!2! + 7!/6!1! + 7!/7!0!
= 21 + 7 + 1
= 29
We can obtain atleast 5 heads in 29 ways
Probability of Atleast 5 heads = 29/128 = 0.23
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