Question

how many ways can the word COSTING
can be arranged such that the vowels do not occour togeher​

Answer 1

Answer:

There are 7 letters in the word STRANGE, of which 2 are vowels. and there are four Odd places (First,third,fifthandseventh) where the two vowels are to be placed.And two vowels may be placed in these 4 places in

4

P

2

=4×3=12 ways. And corresponding to each of these 12 ways the other 5 letters may be placed in the 5 places in 5! ways =5×4×3×2=120 ways.

So the total number of required arrangement

=12×120

=1440ways

(ii)

There are 7 letters. Since the vowels are not to be separated, so we may regard them as forming one letter.

Thus, there are six letters S,T,R,N,G(AE). They can be arranged among them self in 6! ways and two vowels can again be arranged in 2! ways.

So, The total number of arrangement (when vowels are vowels come separated)

=6!×2!=1440ways

(iii)

The number of arrangements in which the vowels do not come together can be obtained by subtracting from the total number of arrangements in which the vowels come together.

Now, the total number of arrangements is 7!

And the number of arrangements in which the vowels do not come together

=7!−6!×2!=5040

Therefore, 5040−1440=3600