In the card game Red 7, the deck consists of 49 cards, seven each in the seven c

Question

In the card game Red 7, the deck consists of 49 cards, seven each in the seven colours of the rainbow (red, orange, yellow, green, blue, indigo, violet). There are seven cards numbered 1 through 7 in each colour, so all 49 cards are distinct. You are dealt a hand of seven cards. Answer each question and briefly explain your reasoning. Leave your answer unsimplified in terms of permutations, combinations, factorials, exponents, etc.

(a) (2 points) How many seven-card hands contain one card of each number?

(b) (2 points) How many seven-card hands contain exactly three 7s?

(c) (2 points) How many seven-card hands contain three even numbers and four odd numbers?

(d) (2 points) How many seven-card hands contain exactly two colours?

(e) (2 points) How many seven-card hands contain at least one 3 and at least one 6?

Explanation / Answer

In the card game Red 7, the deck consists of 49 cards, seven each in the seven colours of the rainbow (red, orange, yellow, green, blue, indigo, violet). There are seven cards numbered 1 through 7 in each colour, so all 49 cards are distinct. You are dealt a hand of seven cards. Answer each question and briefly explain your reasoning. Leave your answer unsimplified in terms of permutations, combinations, factorials, exponents, etc.

(a) (2 points) How many seven-card hands contain one card of each number?

Solution:

Deck have 49 cards , seven card of each colour rainbow (red, orange, yellow, green, blue, indigo, violet).Assign the each number to each colour like 1 to 7.

Select 7 cards , which each contains one card of each number that is use the combination of select cards.

Select the cards of each colour = 7C1 * 7C1 * 7C1 * 7C1* 7C1 * 7C1 * 7C1

                                                   = 7 * 7 * 7 * 7 * 7 * 7 * 7

                                                = 77

Thus the seven-card hands contain one card of each number is 77

(d)How many seven-card hands contain exactly two colours?

Solution:

Exactly two colours in the seven-card hands , that means need to find two colours of cards.

Select exactly two colours is = 7C2 * 42C5

Thus the seven-card hands contain exactly two colours is 7C2 * 42C5

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