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**Exercise 7.4**

**1. If find **

**Ans. **Given:

**2. Determine if:**

**(i) **

**(ii) **

**Ans. (i)** Given:

**(ii)** Given:

**3. How many chords can be drawn through 21 points on a circle?**

**Ans. **There are 21 points on the circumference of a circle. Since one and only one chord can be drawn by joining 2 distinct points, therefore the required number of chords given by

**4. In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?**

**Ans. **There are 5 boys and 4 girls and 3 out of 5 boys and 3 out of 4 girls have to be selected.

Number of ways of selection =

= = = 40

**5. Find the number ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.**

**Ans. **There are 6 red balls, 5 white balls and 5 blue balls. 3 balls of each colour have to be found.

Number of ways of selection =

=

= = 2000

**6. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.**

**Ans. **There are 4 aces and 48 other cards in a deck of 52 cards. We have to select 1 ace out of 4 aces and 4 other cards out of 48 other cards.

Number of ways of selection =

=

= = 778320

**7. In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?**

**Ans. **There are 5 bowlers and 12 other players in a team of 17 players we have to select 4 bowels out of 5 bowlers and 7 other players out of 12 other players.

Number of ways of selection =

=

=

= = 3960

**8. A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.**

**Ans. **There are 5 black and 6 red balls. We have to select 2 black balls out of 5 black balls and 3 red balls out of 6 red balls.

Number of ways of selection = =

= = 200

**9. In how many ways can a student choose a program of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?**

**Ans. **There are 9 courses and number of courses to be selected are 5 in which 2 specific courses are compulsory. 3 courses out of remaining 7 courses have to be selected.

Number of ways of selection = =

= = 35

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