Question

Of the 100 entries in a costume contest, 39 entrants were dressed as heroes and 45 entrants were wearing a mask. If 21 entrants were dressed as heroes wearing a mask, how many entrants were neither dressed as heroes nor wearing a mask?

1. 10
2. 8
3. 11

Answer 1

Correct question with correct options has been attached

Answer:

37

Explanation:

Let C represent those dressed as heroes and let B represent those wearing mask

Thus;

n(C) = 39

n(D) = 45

We are told that 21 entrants were dressed as heroes wearing a mask.

Thus; n(C n D) = 21

We are also told that there were a total of 100 entries.

Thus, n(T) = 100

Now, number of entrants neither dressed as heroes nor wearing a mask is given by;

n(T) - n(C u D)

n(C u D) = n(C) + n(D) - n(C n D)

n(C u D) = 39 + 45 - 21

n(C u D) = 63

Thus;number of entrants neither dressed as heroes nor wearing a mask is: 100 - 63 = 37