Answer:
a) 736 ways.
b) 200 ways.
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!!!