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

Number of digits available = 9

(1, 2, 3, 4, 5, 6, 7, 8, 9)

Number of digits to be used = 3

(No digit is to repeat)

$rightwards double arrow$ n = 9, r = 3

Number of permutations = $space space space straight P presuperscript 9 subscript 3 space equals space fraction numerator 9 factorial over denominator 6 factorial end fraction space equals space fraction numerator 9 cross times 8 cross times 7 cross times 6 factorial over denominator 6 factorial end fraction equals 504$

Hence, the number of 3-digit numbers formed = 504.

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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 ?

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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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