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) : Number of letters = 6 Number of vowels = 2 namely A.E these alphabets can be arrange themselves by 2! ways ∴ Number of words =6!/2! = 360

(b) Treat B and T as a single letter. Then the remaining letters (5 + 1 = 6) can be arranged in 6! ways. Since, O is repeated twice, we...

(a) Reqd. number = 4! × 2! = 24× 2 = 48

(e) The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are...

(c) Taking all vowels (IEO) as a single letter (since they come together) there are six letters Hence no. of arrangements = 6!/2!x3!=2160 [Three vowels can be arranged 3! ways among themselves, hence...

(b) Required number of possible outcomes = Total number of possible outcomes – Number of possible outcomes in which all vowels are together = 6 ! – 4 ! × 3 != 576

(b) First letter can be dropped into any of the 3 boxes. It can be done in 3 ways. Similarly second letter can also be dropped into any of the...

(d) Total no of ways of arrangement for six players = 6! Let us take Ajit and Mukerjee as one entity. So now there are (6 – 2 + 1)...

(D) Letter in the given word Letter in the alphabet series (i) P A R P Q R (ii) A R A D A B C D (iii) A D I S E A B D E

(C) The alphabet is 3.