Question

How many possible ways that we can assign two heads by tossing five coins?

Answer 1

In tossing of five coins we get first head on any of the 5 coins in 5 possible ways. For each way, the other head will appear on any of rest of 4 coins in 4 ways.

Now the number of possible ways in which two heads occur by tossing five coins, provided the 1st and 2nd heads appear on i th and j th coin respectively [i, j=1(1)5, ij], is same if the 1st and 2nd heads appear on j th and i th coins respectively.

Thus, the number of possible ways in which two heads appear by tossing five coins is=(5*4) /2=⁵C₂=10.