Question

The number of different words that can be formed from the letters of the word “TRIANGLE” so that no vowels are together is

A.7200

B.36000

C.14400

D.1240

​

Answer 1

It's 14400

The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels not occur together is

MEDIUM

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ANSWER

The word

′′

TRIANGLE

′′

has 8 letters of which 3 are vowels.

∴ Total words=8!=8×7×6×5×4×3×2×1=40320

No. of words in which two vowels are together. We select two vowels and then tie them together so that we can effectively left with 7 letters and also we need to take care of internal arrangement of two vowels.

∴No. of words in which two vowels are together=3C

2

×7!×2!=3×7×6×5×4×3×2×1×2=30240

But, we need to include words in which three vowels are together.

∴No. of words in which three vowels are together=3C

3

×6!×3!=4320

∴Required no. of words =40320−30240+4320=14400

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Answer 2

Answer:

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