0
$\begingroup$

In one class there are 25 students there are 15 women and 10 men. Select a committee if:

  • A) There must be 3 men and 3 women
  • B) 6 students regardless of gender
  • C) 6 students of the same gender

Approach:

  1. A) 15 *10 *14 * 9 *13 *8 (In the order, woman,male,woman,etc) = 1965600
  2. B) 25C6 = 177100
  3. C) (15C6)* (10C6) = 1051050

Thanks in advance.

  • 1
    Part (A) your answer assumes that order within the committee matters, but it doesn't. Just pick who the three men are, and pick who the three women are. Multiply. Part (B) is correct. Part (C) you multiplied where you shouldn't have. What should you do instead of multiplying? Why do we do this instead of multiplying? – 2017-02-04
  • 0
    I see now @JMoravitz Thanks – 2017-02-05

1 Answers 1

1
A) There must be 3 men and 3 women

$$\dbinom{10}{3}\dbinom{15}{3}$$

B) 6 students regardless of gender

$$\dbinom{25}{6}$$

C) 6 students of the same gender

$$\dbinom{15}{6}+\dbinom{10}{6}$$

  • 0
    Thanks Kiran for your help. – 2017-02-05