Exercise 6.1 answers: Permutations and Combinations

Class 11 Maths6 questions

Exercise 6.1

6 questions · page 104 of the book

Question 1

“How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that” · p. 104

Open NCERT p. 104Matches NCERT’s answer

(i) repetition of the digits is allowed

  1. Each of the 3 digit-places can be filled by any of the 5 digits, since repeating a digit is allowed.
  2. Hundreds place: 5 choices. Tens place: 5 choices. Units place: 5 choices.
  3. Multiply the choices: 5 × 5 × 5 = 125.

Answer125

(ii) repetition of the digits is not allowed

  1. No digit may repeat, so once a digit is used it cannot be used again.
  2. Hundreds place: 5 choices. Tens place: 4 digits are left. Units place: 3 digits are left.
  3. Multiply: 5 × 4 × 3 = 60.

Answer60

Watch this explained “Three from six, before any rule”, 2:02 into Filling a row of places one at a time from a supply of distinct objects

Question 2

“How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated” · p. 104

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  1. A number is even when its units digit is even, so fill the units place first.
  2. Units place: only 2, 4 or 6 can go here — 3 choices.
  3. Hundreds place: any of the 6 digits, since repetition is allowed — 6 choices.
  4. Tens place: any of the 6 digits — 6 choices.
  5. Multiply: 6 × 6 × 3 = 108.

Answer108

Watch this explained “Which stage goes first”, 7:18 into Why choices made one after another multiply rather than add

Question 3

“How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated” · p. 104

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  1. There are 10 letters to choose from and 4 places in the code, with no letter repeated.
  2. First place: 10 choices. Second place: 9 letters left. Third place: 8 letters left. Fourth place: 7 letters left.
  3. Multiply: 10 × 9 × 8 × 7 = 5040.

Answer5040

Watch this explained “Three from six, before any rule”, 2:02 into Filling a row of places one at a time from a supply of distinct objects

Question 4

“How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67” · p. 104

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  1. The first two digits are fixed as 6 and 7, using up two of the ten digits.
  2. That leaves 8 digits (0–9 except 6 and 7) for the remaining 3 places, with no repeats.
  3. Third place: 8 choices. Fourth place: 7 digits left. Fifth place: 6 digits left.
  4. Multiply: 8 × 7 × 6 = 336.

Answer336

Watch this explained “Back to the lock”, 11:15 into Why choices made one after another multiply rather than add

Question 5

“A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?” · p. 104

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  1. Each toss has 2 possible outcomes: heads or tails.
  2. The 3 tosses are independent stages, one after another.
  3. Multiply the choices at each stage: 2 × 2 × 2 = 8.

Answer8

Watch this explained “A third stage”, 4:33 into Why choices made one after another multiply rather than add

Question 6

“Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags” · p. 104

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  1. Each signal uses 2 flags in a definite order (one below the other), with no flag repeated.
  2. First flag: 5 choices. Second flag: 4 flags are left.
  3. Multiply: 5 × 4 = 20.

Answer20

Watch this explained “When you must add instead”, 8:52 into Why choices made one after another multiply rather than add

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.

All the videos for Chapter 6 →