2 There are 4 men and 6 women candidates for a job In how ma

2. There are 4 men and 6 women candidates for a job. In how many ways

a. We can select 3 people as a president, vice president, and a secretary?

b. How many committees of 5 with exactly 2 men are possible?

3.

a. What is the probability of a five-card poker hand contains two hearts?

b. What is the probability of a five-card poker hand contains 2 Aces and 2 kings?

Solution

2. There are 4 men and 6 women candidates for a job.

a. Hence there are a total of 10 candidates. Therefore, number of ways in which 3 people can be selected as a president, vice president, and a secretary is 10 x 9 x 8 = 720 ways.

b. Number of committees of 5 with exactly 2 men are ⁴C₂ = 6

3. In a pack of 52 cards, there are 13 cards of same suit and since there are 4 suits, there are 4 cards of same rank.

a. The probability of a five-card poker hand contains two hearts is (13/52) x (12/51) x (39/50) x (38/49) x (37/48) = 0.0274

b. The probability of a five-card poker hand contains 2 Aces and 2 kings is (4/52) x (3/51) x (4/50) x (3/49) x (44/48) = 0.00002