Question 1a) How many possible combinations of $5$ card poker hands are there?
Answer : $\binom{52}5$ – basically the combination formula : $$\frac{N!}{(N-r)!r!}$$
(this is correct because we did it in class)
I need help on this question : How many combinations of $5$ cards contain only diamonds?
My Answer : $\binom{52}5 – \left[\binom{52}{13}+\binom{52}{13}+\binom{52}{13}\right]$
Is it correct? If not, what is the correct answer?
Best Answer
Why choose from 52 cards? You are asked to find the number of 5 card hands from a single suit i.e from 13 cards. Use the same formula as in (1) such that you have $C(13,5)$.