NCERT Solutions class-11 Maths Exercise 7.4

Exercise 7.4

1. If find

Ans. Given:

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2. Determine if:

(i)

(ii)

Ans. (i) Given:

(ii) Given:

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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

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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

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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

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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

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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

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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

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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