In a card game player get at the start 2 green cards, 3 blue cards, 4 red cards, and 3 yellow cards. In how many ways can the player get cards at the start if this card game has 7 green, 7 blue, 10 red and 10 yellow cards?
To find the number of ways the player can get cards at the start, we need to calculate the number of combinations of cards they can have.
In this case, we have 7 green cards, and the player already has 2, so they can choose 5 more green cards from the remaining 5.
The number of combinations for green cards = C(5, 5) = 1
Similarly, for blue cards, we have 7 blue cards, and the player already has 3, so they can choose 4 more blue cards from the remaining 4.
The number of combinations for blue cards = C(4, 4) = 1
For red cards, we have 10 red cards, and the player already has 4, so they can choose 6 more red cards from the remaining 6.
The number of combinations for red cards = C(6, 6) = 1
Lastly, for yellow cards, we have 10 yellow cards, and the player already has 3, so they can choose 7 more yellow cards from the remaining 7.
The number of combinations for yellow cards = C(7, 7) = 1
To find the total number of ways the player can get cards at the start, we multiply the number of combinations for each color together:
Total number of ways = 1 * 1 * 1 * 1 = 1
Therefore, there is only 1 way in which the player can get cards at the start in this card game.