In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
120
720
4320
2160
Twelve students compete for a race.The number of ways in which first three places can be taken as
3!
12.11.10
12!/3!
12! - 3
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
40
400
5040
2520
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
32
48
64
96
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
210
1050
25200
21400
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?
36
60
The value of n, when nP2 = 20 is
3
4
6
5
The number of different four digit numbers that can be formed with the digits 2,3,4,5,7 using each digit only once is.
4!
4 (4!)
5!
5 (7!)
If nP5 = 60.n - 1 P3 , then n is.
15
10
12
P (10, r) = 2 P (9, r), r is equal to
2