How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if all letters are used but first is a vowel ?

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Solution

Total number of vowels in the word MONDAY $= 2$

Number of ways in which first is a vowel = ${2_{C}}_{1}$

And another letters are ${5_{C}}_{5} = 5! = 120$

Therefore, total number of ways = $120 \times {2_{C}}_{1} = 120 \times 2 = 240 w a y s$

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How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if all letters are used but first is a vowel ?

Total number of vowels in the word MONDAY =2Number of ways in which first is a vowel = 2C1And another letters are 5C5=5!=120Therefore, total number of ways = 120×2C1=120×2=240 ways

Total number of vowels in the word MONDAY $= 2$

Number of ways in which first is a vowel = ${2_{C}}_{1}$

And another letters are ${5_{C}}_{5} = 5! = 120$

Therefore, total number of ways = $120 \times {2_{C}}_{1} = 120 \times 2 = 240 w a y s$