general Maths Puzzle

In how many different ways can the letters of the word 'CORPORATION' be arranged
so that the vowels always come together ?

(a)810
(b)1440
(c)2880
(d)50400
(e)5760

Read Solution (Total 1)

50400

In the word 'CORPORATION', we treat the vowels OOAIO as one letter.

Thus, we have CRPRTN (OOAIO).

This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.

Number of ways arranging these letters = 7! = 2520.
2!

Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5!/3! = 20 ways.

Required number of ways = (2520 x 20) = 50400.
12 years agoHelpfull: Yes(2) No(0)

general Other Question

Two angles of a triangle are in the ratio 2:3. Remaining angle the largest one is twice the smallest angle of the triangle.What is the measure of the largest angle of a parallelogram, if the largest angle of the triangle is equal to the smallest angle of the parallelogram ? In how many different ways can the letters of the word 'DETAIL' be arranged
in such a way that the vowels occupy only the odd positions ?

(a)32
(b)48
(c)36
(d)60
(e)120