If the letters of the word ''REGULATIONS'' be arranged at random, find the probability that there will be exactly four letters between the R and the E.

A and B stand in a ring along with 10 other pèrsons. If the arrangement is at random, the probability that there are exactly 3 persons between A and B , is

if letters of the word MATHEMATICS are arranged then the probability that C come before E,E before H ,H before I and I before S

A letter is taken at random from the letters of the word GANGA" and another letter is taken at random from the letters of the word BANGA .The probability that the selected letters are the same is:

If the letters of word "EQUATION" are arranged, find the number of arrangements in which no two consonants are adjacent.

From the English alphabers one letter is chosen at random. What is the probability that it is a vowel?

In how many ways can the letters of the word PENCIL be arranged so that N is always next of E.

In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S, (ii) vowels are all together, (iii) there are always 4 letters between P and S?

The number of ways in which the letters of the word ARRANGE be arranged so that (i) the two R's are never together, (ii) the two A's are together but not two R's. (iii) neither two A's nor two R's are together.

A letter is taken at random from the letters of the word 'ASSISTANT' and another letter is taken at random from the letters of the word 'STATISTICS'. The probability that the selected letters are the same is