Exercise 6.2 answers: Permutations and Combinations

Class 11 Maths5 questions

Exercise 6.2

5 questions · page 106 of the book

Question 1

“Evaluate (i) 8 ! (ii) 4 ! – 3 !” · p. 106

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(i) 8 !

  1. 8! means the product of all whole numbers from 1 to 8.
  2. 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8.
  3. Working it out, 8! = 40320.

Answer40320

(ii) 4 ! – 3 !

  1. 4! = 1 × 2 × 3 × 4 = 24.
  2. 3! = 1 × 2 × 3 = 6.
  3. 4! − 3! = 24 − 6 = 18.

Answer18

Watch this explained “A name for a product you already make”, 0:00 into A shorthand for descending products, and why the empty product is set to one

Question 2

“Is 3 ! + 4 ! = 7 ! ?” · p. 107

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  1. 3! = 1 × 2 × 3 = 6.
  2. 4! = 1 × 2 × 3 × 4 = 24.
  3. 3! + 4! = 6 + 24 = 30.
  4. 7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040.
  5. 30 is not equal to 5040, so 3! + 4! is not equal to 7!.

AnswerNo — 3! + 4! = 30, which is not equal to 7! = 5040.

Watch this explained “It does not carry across a plus”, 10:12 into A shorthand for descending products, and why the empty product is set to one

Question 3

“Compute 8!/(6! × 2!)” · p. 107

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  1. 8! = 6! × 7 × 8, so 8!/6! = 7 × 8 = 56.
  2. 2! = 1 × 2 = 2.
  3. Divide: 56 ÷ 2 = 28.

Answer28

Watch this explained “Cancelling instead of computing”, 7:12 into A shorthand for descending products, and why the empty product is set to one

Question 4

“If 1/6! + 1/7! = x/8!, find x” · p. 107

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  1. Write 7! as 7 × 6!, so 1/7! = 1/(7 × 6!).
  2. Multiply every term by 8! = 8 × 7 × 6!: 8!/6! = 56, and 8!/7! = 8.
  3. So the left side becomes 56 + 8 = 64.
  4. This equals x, so x = 64.

Answer64

Watch this explained “An unknown over a factorial”, 11:01 into A shorthand for descending products, and why the empty product is set to one

Question 5

“Evaluate n! / (n-r)!, when (i) n = 6, r = 2 (ii) n = 9, r = 5” · p. 107

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(i) n = 6, r = 2

  1. n!/(n−r)! = 6!/(6−2)! = 6!/4!.
  2. 6!/4! = 6 × 5 = 30, since the 4! cancels.

Answer30

(ii) n = 9, r = 5

  1. n!/(n−r)! = 9!/(9−5)! = 9!/4!.
  2. 9!/4! = 9 × 8 × 7 × 6 × 5 = 15120.

Answer15120

Watch this explained “Cancelling instead of computing”, 7:12 into A shorthand for descending products, and why the empty product is set to one

Every question here was solved twice, separately, by two different AI models, and each answer was put back into the question by a computer program to check it. Where the two disagreed, a stronger model solved it again and the computer check had to pass on its answer. A question about reasoning rather than a number is shown as “one way to think about it”, and anything not yet proven says so instead of guessing. Each answer links to the moment in the video that teaches it.

We quote only enough of each question to find it: keep your NCERT book open, or open this chapter in NCERT’s PDF. Spotted a mistake? Tell us.

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