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Permutation And Combination Questions

Questions based on permutation and combinations are confusing to many of the students as they are always unclear about whether need to calculate permutations or combinations. The topic is very important as the concept is also used to solve many probability questions. Therefore let me clarify here the difference between both the terms so that going forward you can solve permutation and combination questions like an expert.

Combinations can be defined as the number of ways in which r things can be selected out of n things at a time. The keyword here is SELECTION. The order in which r things are selected does not matter. So AB and BA are same in this case.

Permutations can be defined as the number of ways in which r things can be selected and arranged out of n things at a time. The keyword here is ARRANGEMENT. The order in which r things are arranged has the critical importance. So AB and BA are different in this case.

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

  1. 5
  2. 10
  3. 15
  4. 20
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How many 3 digit numbers greater than 400 can be made with the digits 2,3,4,0,5,6 ? (Digits cannot be repeated)

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How many 3 digit numbers between 300 and 500 can be made with the digits 1,2,3,0,4, 5,6 ? (Digits cannot be repeated)

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How many 3 digit odd numbers can be made with the digits 0,2,3,4,6,7 ? (Digits cannot be repeated)

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How many 3 digit even numbers can be made with the digits 0,2,3,4,6,7 ? (Digits cannot be repeated)

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In how many ways can the letters of the word ‘LEADER’ be arranged ?

  1. 72
  2. 144
  3. 360
  4. 720
  5. None of these
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In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

  1. 10080
  2. 4989600
  3. 120960
  4. None of these
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In how many different ways the letter of the word “ASSASSINATION” can be arranged, so that all the ‘S’ are together ?

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In how many different ways can the letters of the word “DETAIL” be arranged in such a way that the vowels occupy only the odd positions ?

  1. 32
  2. 48
  3. 36
  4. 60
  5. 120
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In how many different ways can the letters of the word ‘OPTICAL’ be arranged if it starts with letter T?

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In how many different ways the letter of the word “BANKING” can be arranged if it starts with vowel ?

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