How many ways are there to pick 3 different cards from a standard 52 card deck such that: (Each of the following parts is independent of the others.)

(a). The first card is a Jack, the second card is a King and the third card is not a Queen.
(b). The first card is a Jack, the second is a King and the third card is a spade.

a) 736 ways.

b) 200 ways.

Step-by-step explanation:

In a deck of cards, there 52 cards in total.

- There are 4 Jacks.

- There are 4 Kings.

- There are 4 Queens; number of non-Queen cards = 48

- There are 13 spades.

a) The first card is a Jack, the second card is a King and the third card is not a Queen.

This would be evaluated as saying, if we pick a Jack and then a King, the number of non-queen cards that remain becomes 48-2 = 46.

So, the number of ways that one can pick a Jack, a King and a non-queen card is given as

4 × 4 × 46 = 736 ways

b) The first card is a Jack, the second is a King and the third card is a spade.

This is a Bit more complicated because there is a Jack card that is also a spade card and there is a King card that is also a spade card.

So, the number of ways this can happen will be a sum of carefully thought about ways.

- Selected Jack is a spade, selected King is also a spade.

Number of ways = 1 × 1 × 11 = 11

- Selected Jack is not a spade, selected King is a spade.

Number of ways = 3 × 1 × 12 = 36

- Selected Jack is a spade, selected King is not a spade.

Number of ways = 1 × 3 × 12 = 36

- Selected Jack is not a spade, selected King is also not a spade.

Number of ways = 3 × 3 × 13 = 117

Total number of ways of selecting the first card as a Jack, the second as a King and the third card as a spade = 11 + 36 + 36 + 117 = 300 ways.

Hope this Helps!!!

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong