Twelve coins are tossed and placed in a line. Each coin can show either a head or a tail.
- Find the number of different arrangements of heads and tails which can be obtained.
- Find the number of different arrangements which contain 7 heads and 5 tails.
Solution
Each coin can show either a head or a tail, giving 2 possibilities per coin. For 12 coins, the total number of arrangements is given by:
\(2^{12} = 4096\)
To find the number of arrangements with 7 heads and 5 tails, use the combination formula:
\(\binom{12}{7} = \frac{12!}{7!5!} = 792\)
Log in to record attempts.