NCERT Solutions for Class 11 Maths Exercise 7.4 of the Chapter 7 Permutaion and Combination

 

NCERT Solutions for Class 11 Maths Exercise 7.4 of the Chapter 7 Permutaion and Combination are available here for boosting the preparation of class 11 maths exam. The NCERT Solutions for Class 11 Maths Exercise 7.4 of the Chapter 7 Permutaion and Combination are created by an expert of maths who has huge experience in teaching maths from class 9 to class 12.All the questions of permutation and combination are solved by step by step ways therefore every students of the grade 11 can understand the solutions easily .

NCERT Solutions for Class 11 Maths  Chapter 7 Permutation and Combination

Exercise 7.1- Permutations and Combinations

Exercise 7.2 -Permutation and Combination

Exercise 7.3-Permutation and Combination

Exercise 7.4-Permutation and Combination

Miscellaneous Exercise-Permutation and Combination

NCERT Solutions for Class 11 Maths Exercise 7.4 of the Chapter 7 Permutation and Combination

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Q1. If ⁿC₈ = ⁿc₂, find  ⁿc₂

Ans. Since ⁿC_r =ⁿC_n-r

∴ⁿC₈ = ⁿC_n-8, 

Substituting ⁿC₈ = ⁿC_n-8,

ⁿC_n-8 = ⁿc₂

n – 8 = 2⇒ n = 10

Hence the required value of  ⁿc₂is 45

Q2.Determine n if

(i) ²ⁿC₃: ⁿc₃ = 12 : 1

(ii) ²ⁿC₃: ⁿc₃ = 11 : 1

Ans. It is given to us that

²ⁿC₃: ⁿc₃ = 12 : 1

 

 

4(2n -1)(n -1) : (n -1)(n -2) = 12 : 1

8n -4 = 12n – 24

4n = 20

n = 5

(ii) ²ⁿC₃: ⁿc₃ = 11 : 1

Similarly as in (i),we have

11n – 22 = 8n – 4

3n = 18

n = 6

Q3. How many chords can be drawn through 21 points on a circle?

Ans.For drawing chords we are required to choose two points out of 21 points on the circle, therefore the number of ways of such combinations are  ²¹C₂

The number of chords are = ²¹C₂

Hence total number of chords can be drawn are  210

Q4.In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls.

Ans. The number of ways 3 boys can be selected out of 5 boys are ⁵C₃

The number of ways 3 girls can be selected out of 4 girls are ⁴C₃

According to the multiplication rule,total number of ways selecting  a team of 3 boys and 3 girls are = ⁵C₃ ×⁴C₃

Hence the number of ways  a team of 3 boys and 3 girls  selected from 5 boys and 4 girls is 40

Q5.Find the number of 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. The number of ways of selecting 3 balls out of 6 red balls are  ⁶C₃

The number of ways of selecting 3 balls out of 5 white balls are  ⁵C₃

The number of ways of selecting 3 balls out of 5 blue balls are  ⁵C₃

According to the multiplication rule,total number of ways selecting  9 balls out of 6 red ball,5 white balls and 5 blue balls are = ⁶C₃ ×⁵C₃ ×⁵C₃

= 20 × 10 × 10 = 2000

Hence required number of ways of selecting 9 balls are 2000

Q6.Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Ans. The number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination are =The number of ways selecting 1 ace out of 5 cards × The number of ways selecting remaining 4 cards out of remaining (52 -4= 48 ) cards

The number of ways selecting 1 ace out of 4 cards = ⁴C₁

The number of ways selecting  remaining 4 cards out of  remaining (52 -4 = 48) cards = ⁴⁸C₄

The number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination are = ⁴C₁ × ⁴⁸C₄

= 4× 2× 47 ×46 ×45 = 778320

The number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination is 778320

Q7.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.The number of ways selecting  a team of 11 players = The number of ways selecting 4 bowlers out of 5 bowlers × The number of ways selecting 7 players out of remaining (17-5 =12) players

The number of ways selecting  a team of 11 players = ⁵C₄×¹²C₇

=5 × 11×9×8 = 3960

The number of ways selecting  a team of 11 players in which there are exactly 4 bowlers is  3960

Q8.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.The number of ways selecting 2 black balls out of 5 black balls = ⁵C₂

The number of ways selecting 3 red balls out of 6 red balls = ⁶C₃

The number of ways selecting 2 black balls and 3 red balls out of 5 black balls and 6 red balls =⁵C₂ ×  ⁶C₃

= 10 × 20 = 200

The number of ways selecting 2 black balls and 3 red balls out of 5 black balls and 6 red balls is 200

Q9.In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Ans. It is given that student has to choose 5 coarses out of 9 coarses in which 2 coarses are compulsury.

Since 2 coarses are compusury therefore number of ways selecting 5 coarses = Number of ways of selecting  remaining (5 -2 = 3)  coarses out of remaining (9 -2 = 7) coarses is = ⁷C₃

Hence required number of ways selecting 5 coarses is 35

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