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Permutations and Combinations

Short Answer Type

71. How many 3-digit numbers can be formed by using digits 1 to 9 if no digit is repeated?

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72.

How many 4-digit numbers are there if no digit is repeated?

How many numbers are there between 1000 and 9999 so that no digit is repeated?

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73. How many words with or without meaning can be formed using all the letters of the word ‘EQUATION’ using each letter exactly once?

Additional part: How many of these words begin with E and end with N?

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74. How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if 4 letters are used at a time.

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75. How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if all letters are used at a time.

rightwards double arrow

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76. How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if all letters are used but the first letter is a vowel?

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77. How many words, with or without meaning, can be formed with the letters of word ‘MONDAY’ assuming, that no letter is repeated, if 4 letters are used but the first letter is a vowel ?

Number of letters in word 'MONDAY' = 6 (all district)

Number of vowels = 2 (O and A)

Number of letters to be used in 4 and first letter is a vowel,

$rightwards double arrow$

Number of arrangements for box 1 = $straight P presuperscript 2 subscript 1 space equals space fraction numerator 2 factorial over denominator 1 factorial end fraction equals 2$ (i)
(Two vowels for 1 box)

We now have 5 letters left and 3 boxes for them.

$rightwards double arrow$ n = 5, r = 3

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Hence, from (i) and (ii), the total number of permutations i.e., the number of words formed:

= 2 x 60 = 120.

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78.

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

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79.

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that no two consonants are together.

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80. In how many ways can 6-girls and 4 boys be seated in a row so that no two boys are together?

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