Question

2)How many poker hands consist of three clubs and two cards that are not clubs?
A. C(13,3) C(39,2)
B. C(52,3) C(39,2)
C. C(52,3) C(49,2)
D. C(13,3) C(49,2)
E. None of these

3)Write the negation of the following statement. The band does not have a guitarist or the band plays rock music. Choose the correct answer below.
A. The band has a guitarist or the band does not play rock music.
B. If the band has a guitarist then the band does not play rock music.
C. The band does not have a guitarist or the band does not play rock music.
D. The band has a guitarist and the band does not play rock music.

Answer 1

2) We have to find the number of poker hands which consists of three clubs and two cards that are not clubs. We know that a deck of cards contain 52 cards. There are 4 suits in these 52 cards : club, heart, spade, diamond. All the suits consists of 13 cards. Thus, there are 13 clubs. So, we have to select 3 clubs from these 13 clubs. We can select 3 clubs from 13 clubs in 13C3 ways. Now, among the 52 cards, 13 cards are clubs. Thus, the number of cards which are not clubs = 52 - 13 = 39. We have to select 2 cards from these 39 cards. Thus, we can select 2 cards from these 39 cards in 39C2 ways.

Thus, number of ways = (13C3)*(39C2). This can also be written as C(13,3) C(39,2).

Thus, the number of poker hands which consists of three clubs and two cards that are not clubs = C(13,3) C(39,2).

Thus, the correct option is (A).

As per Chegg guidelines we can solve only one question.