Question

A normal coin is tossed ten times and the result, heads or tails, is recorded for each toss. how many of the possible outcomes have three heads and seven tails? (we mean to count the different orderings on the 10 flips, and not simply the number of heads and tails that appear)

i used nCr and i got the answer 120 oucomes. is that correct?

Answer 1

120 is correct and the formula to be used is 10C₃ or 10C₇ both of which work out to 120

Explanation:

That appears to be correct . Since only one of two possibilities exist for each toss, for 10 tosses we determine if 3 heads appear that would be the same as 7 tails appearing for the 10 tosses

Number of ways r heads can appear in n tosses is indeed nCr

For r= 3 heads and n = 10 tosses this would be

10C₃ = 120

This should be the same as 10C₇ which works out to 120 also