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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?

99 Views

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?

108 Views

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.

103 Views

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?

101 Views

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 ?

145 Views

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?

Number of letters = (all distinct)

Number of vowels = 5 (e, i, o, u, a)

Number of consonants = 3 (q, t, n)

Step I: Tie the vowels together

$rightwards double arrow$ Number of permutations = $straight P presuperscript 5 subscript 5 equals space 5 factorial space equals space 120$

Step II: Tie the consonants together.

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Step III: Mix the bundles and any remaining letter to give 1 + 1 + 0 = 2 letters.

Number of permutations = $space space straight P presuperscript 2 subscript 2 equals 2 factorial comma space equals space 2$

Hence, the number of permutations, using, fundamental principle of counting

= 120 x 6 x 2 = 1440