Commerce Exam  >  Commerce Notes  >  Mathematics (Maths) Class 11  >  NCERT Solutions: 6.4 - Permutations And Combinations

NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

Q1: If NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations, find NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations.
Ans: It is known that, NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

Therefore,

 NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

 NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

Q2: Determine n if  (i)  NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations    (ii)NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations
Ans: (i)

 NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

(ii)

 NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

⇒ 11n – 8n = - 4+ 22  
⇒ 3n = 18
⇒ n = 6

Q3: How many chords can be drawn through 21 points on a circle?
Ans: For drawing one chord on a circle, only 2 points are required.
To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted.
Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time.
Thus, required number of chords = NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

Q4: In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Ans: A team of 3 boys and 3 girls is to be selected from 5 boys and 4 girls.
3 boys can be selected from 5 boys in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
3 girls can be selected from 4 girls in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
Therefore, by multiplication principle, number of ways in which a team of 3 boys and 3 girls can be selected
 NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

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: There are a total of 6 red balls, 5 white balls, and 5 blue balls.
9 balls have to be selected in such a way that each selection consists of 3 balls of each colour.
Here,
3 balls can be selected from 6 red balls in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
3 balls can be selected from 5 white balls in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
3 balls can be selected from 5 blue balls in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
Thus, by multiplication principle, required number of ways of selecting 9 balls

 NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

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: In a deck of 52 cards, there are 4 aces. A combination of 5 cards have to be made in which there is exactly one ace.
Then, one ace can be selected in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways and the remaining 4 cards can be selected out of the 48 cards in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
Thus, by multiplication principle, required number of 5 card combinations
NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

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: Out of 17 players, 5 players are bowlers.
A cricket team of 11 players is to be selected in such a way that there are exactly 4 bowlers.
4 bowlers can be selected in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways and the remaining 7 players can be selected out of the 12 players in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
Thus, by multiplication principle, required number of ways of selecting cricket team NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

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: There are 5 black and 6 red balls in the bag.
2 black balls can be selected out of 5 black balls in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways and 3 red balls can be selected out of 6 red balls in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
Thus, by multiplication principle, required number of ways of selecting 2 black and 3 red balls NCERT Solutions Class 11 Maths Chapter 6 - Permutations and CombinationsNCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

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: There are 9 courses available out of which, 2 specific courses are compulsory for every student.
Therefore, every student has to choose 3 courses out of the remaining 7 courses. This can be chosen in NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations ways.
Thus, required number of ways of choosing the programmeNCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

The document NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations is a part of the Commerce Course Mathematics (Maths) Class 11.
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FAQs on NCERT Solutions Class 11 Maths Chapter 6 - Permutations and Combinations

1. How do permutations and combinations differ from each other?
Ans. Permutations refer to the arrangement of objects in a specific order, while combinations refer to the selection of objects without considering the order.
2. What is the formula for calculating permutations of objects?
Ans. The formula for calculating permutations of objects is given by nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.
3. How can permutations and combinations be applied in real-life scenarios?
Ans. Permutations and combinations are commonly used in various fields such as probability, statistics, and computer science to solve problems related to arrangements and selections of objects.
4. What are the key differences between a permutation and a combination problem?
Ans. In a permutation problem, the order of objects matters, while in a combination problem, the order does not matter. Permutations involve arrangements, while combinations involve selections.
5. Can permutations and combinations be used interchangeably in all situations?
Ans. No, permutations and combinations cannot be used interchangeably in all situations. It is important to identify whether the problem involves arranging objects in a specific order (permutations) or selecting objects without considering the order (combinations) before applying the appropriate formula.
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