# A coin is tossed 8 times. In how many ways can we obtain 4 heads and 4 tails? - Mathematics and Statistics

Sum

A coin is tossed 8 times. In how many ways can we obtain 4 heads and 4 tails?

#### Solution

A coin is tossed 8 times. All heads are identical and all tails are identical.
We can obtain 4 heads and 4 tails in (8!)/(4!4!)

= (8 xx 7 xx 6 xx 5 xx 4!)/((4 xx 3 xx 2 xx 1)4!)

= 2 × 7 × 5
= 70 ways

∴ In 70 different ways, we can obtain 4 heads and 4 tails

Concept: Permutations When All Objects Are Not Distinct
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.4 | Q 3. (i) | Page 82