**Peta deals with a hand of 10 cards from a well-shuffled pack of ordinary playing cards.**

Show that the probability that she deals exactly 5 spades is less than 5%.Show that the probability that she deals exactly 5 spades is less than 5%.

There are 52 cards all together, out of which 13 are spades so the probability of getting a spade would be 1/4, which is 0.25.

So the probability of dealing exactly 5 spades out of 10 would be, using the formula for binomial distribution, (10C5)*(0.25^5)*(0.75^5) = 0.0584 (3 s.f.), which is not less than 0.05.

However, the answer section for this question in the textbook says that the answer is:

0.0468... = 4.7 % (2 s.f.) < 5 %.

But I have no idea how they got this figure because the book does not show any working, and I do not understand why I cannot use binomial for this question.

I would much appreciate it if someone can help me to understand why I cannot use binomial here and why the probability is about 4.7 % as above.

Or am I correct and the textbook is wrong?

Thank you.

(P.S. This question is under the chapter "Probability" in the textbook, which is placed BEFORE the chapter for "Binomial Distribution", therefore, there is supposed to be a way to work it out without using binomial formula)