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?
Assuming the cards of each color are unique, that would be
7C2 * 7C3 * 10C4 * 10C3
= 7*6/1*2 * 7*6*5/1*2*3 * 10*9*8*7/1*2*3*4 * 10*9*8/1*2*3
= 21 * 35 * 210 * 120 = 18 522 000
To determine the number of ways the player can get cards at the start, we need to understand the concept of combinations.
In this card game, the player has a certain number of cards of each color available and needs to select a specific number of cards during the initial draw.
To calculate the number of ways to get the cards at the start, we can use combinations:
1. For the green cards: The player has to choose 2 cards out of the given 7 green cards. Therefore, we calculate "7 choose 2" denoted as C(7, 2).
C(7, 2) = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21
So, there are 21 ways to select 2 green cards.
2. For the blue cards: The player has to choose 3 cards out of the given 7 blue cards. We calculate "7 choose 3" denoted as C(7, 3).
C(7, 3) = 7! / (3! * (7-3)!) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
Therefore, there are 35 ways to select 3 blue cards.
3. For the red cards: The player has to choose 4 cards out of the given 10 red cards. We calculate "10 choose 4" denoted as C(10, 4).
C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
Hence, there are 210 ways to select 4 red cards.
4. For the yellow cards: The player has to choose 3 cards out of the given 10 yellow cards. We calculate "10 choose 3" denoted as C(10, 3).
C(10, 3) = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Therefore, there are 120 ways to select 3 yellow cards.
To find the total number of ways the player can get cards at the start, we multiply the number of ways for each color since these events are independent:
Total ways = 21 * 35 * 210 * 120 = 1,029,600
Hence, there are 1,029,600 ways the player can get cards at the start in this specific card game.