Question

find the number of all possible arrangements of the letter of the word triangle
a)40320
b) 2880
c)720
d) none ​

Answer 1

Answer:

correct option is

c

14400

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