Please help. Consider a deck of 52 playing cards, in how many ways can you draw an ace card, any heart card and a queen card in three draws respectively with replacement?
since there are 4 of each card, what is the chance of drawing an ace first?
Multiply that by the chance of drawing the others. Each draw is independent of the other draws.
To find the number of ways to draw an ace card, any heart card, and a queen card in three draws with replacement from a deck of 52 playing cards, we can break down the problem into three steps:
1. Find the number of ways to draw an ace card:
Since there are 4 ace cards in a deck, we have 4 options to choose an ace card in each draw. As there are three draws with replacement, the total number of ways to draw an ace card is 4 * 4 * 4 = 64.
2. Find the number of ways to draw any heart card:
There are 13 heart cards in a deck, so we have 13 options to choose a heart card in each draw. As there are three draws with replacement, the total number of ways to draw any heart card is 13 * 13 * 13 = 2197.
3. Find the number of ways to draw a queen card:
There are 4 queen cards in a deck, so we have 4 options to choose a queen card in each draw. As there are three draws with replacement, the total number of ways to draw a queen card is 4 * 4 * 4 = 64.
Now, to find the total number of ways to satisfy all the conditions, we need to multiply the results of each step together:
Total number of ways = Number of ways to draw an ace card * Number of ways to draw any heart card * Number of ways to draw a queen card
= 64 * 2197 * 64
= 9,007,616.
Therefore, there are 9,007,616 ways to draw an ace card, any heart card, and a queen card in three draws respectively with replacement from a deck of 52 playing cards.