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Find the number of words each consisting of 3 vowels and 3 con

Question

Find the number of words each consisting of $3$ vowels and $3$ consonants that can be formed from the letters of the word $Circumference$ .

22100

40020

32400

64000

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Asher Discussed

Find the number of words each consisting of

3

vowels and

3

consonants that can be formed from the letters of the word

Circumference

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

There are

3 C^{'} s

Number of ways to arrange the consonant

Case : involving

3^{'} C^{'} s, 2^{'} C s, 1 C, 1 C

and

2 R^{'} s

1 + 12 + 36 + 3 + 9 + 24 = 85

Therefore consonants can be arranged in

85

ways

Arrangements of vowels

= 13

Number of ways of arranging

3

vowels and

3

consonants

=^{6} C_{3} = 20

\Rightarrow

Total number

= 85 \times 13 \times 20 = 22100

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Question Text	Find the number of words each consisting of $3$ vowels and $3$ consonants that can be formed from the letters of the word $Circumference$ .
Answer Type	Text solution:1
Upvotes	150