a) $$\frac{{6!}}{2}$$
b) 3! × 3!
c) $$\frac{{4!}}{2}$$
d) $$\frac{{4! \times 3!}}{{2!}}$$
Answer: d
Explanation: ABACUS is a 6 letter word with 3 of the letters being vowels.
If the 3 vowels have to appear together as stated in the question, then there will 3 consonants and a set of 3 vowels grouped together.
One group of 3 vowels and 3 consonants are essentially 4 elements to be rearranged.
The number of possible rearrangements is 4!
The group of 3 vowels contains two a s and one u
The 3 vowels can rearrange amongst themselves in $$\frac{{3!}}{{2!}}$$ ways as the vowel a appears twice.
Hence, the total number of rearrangements in which the vowels appear together are:
$$\frac{{4! \times 3!}}{{2!}}$$
Related Posts
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language ?
A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:
Join The Discussion