Contents

- 1 How many different ways can the letters of the word mathematics be arranged so that the vowels always come together?
- 2 How many words can be formed out of letters of the word mathematics in how many of these words are consonants together?
- 3 How many ways can parallel be arranged?
- 4 How many ways can the word leader be arranged?
- 5 How many three letter words are formed using the letters of the word time?
- 6 How many consonants are in the word mathematics?
- 7 How many 3 letter words with or without meaning can be formed?
- 8 How many distinct ways can letters be arranged?
- 9 How many ways 5 towels can be put into 4 boxes?
- 10 How many ways can we arrange all the letters such that the last two letters are vowels?
- 11 How many permutations are in the word banana?
- 12 How many words can be formed by 2 vowels and 3 consonants out of 4 vowels and 7 consonants?
- 13 How many 4 letter words with or without meaning can be formed logarithms?

## How many different ways can the letters of the word mathematics be arranged so that the vowels always come together?

In 4989600 distinct ways, the letter of the word ‘ Mathematics ‘ can be written. (i) When vowels are taken together: In the word ‘ Mathematics ‘, we treat the vowels A, E, A, I as one letter. Thus, we have MTHMTCS (AEAI).

## How many words can be formed out of letters of the word mathematics in how many of these words are consonants together?

(i) There are 11 letters in the word ‘ MATHEMATICS ‘. Out of these letters M occurs twice, A occurs twice, T occurs twice and the rest are all different. =11! (2!)

## How many ways can parallel be arranged?

PARALLEL has 8 letters with one letter appearing 3 times and 1 letter appearing 2 times. The letters can be arranged in 8!/(3!* 2!) = 3360 ways.

## How many ways can the word leader be arranged?

In how many ways can the letters of the word ‘LEADER’ be arranged? E. 6! = 360.

## How many three letter words are formed using the letters of the word time?

How many three letter words are formed using the letters of the word TIME? Explanation: The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24.

## How many consonants are in the word mathematics?

The fraction of the consonants in the word ‘ mathematics ‘ is 7/11. There are a total of 11 letters in the word, of which 4 (a, e, a, i) are vowels and 7 (m, t, h, m, t, c, s) are consonants.

## How many 3 letter words with or without meaning can be formed?

= 720. Hence, the no. of 3 letter words formed from the word LOGARITHMS without repetition is 720. Hence the correct option of this question is option (a).

## How many distinct ways can letters be arranged?

= 2494800 ways of arranging it.

## How many ways 5 towels can be put into 4 boxes?

Since there are 5 letters and each letter can be posted in 4 ways. So, total number of ways in which all the five letters can be posted = 4 × 4 × 4 × 4 × 4 = 45.

## How many ways can we arrange all the letters such that the last two letters are vowels?

If the last letter also has to be a vowel, then it can be any one of the remaining 3 vowels. After we have selected the two vowels for the first and last positions, we have 6 letters left, of which 2 repeat. Thus, the number of ways to arrange these in-between letters is 6!/ 2! = 720/ 2 = 360.

## How many permutations are in the word banana?

B – 1 A – 3 N – 2 So total no of words possible is factorial(6) ie 6! but we must remove duplicate words: ie- (6!/(2!* 3!)) which gives 60 So 60 distinguishable permutation of the letters in BANANA.

## How many words can be formed by 2 vowels and 3 consonants out of 4 vowels and 7 consonants?

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? = 210.

## How many 4 letter words with or without meaning can be formed logarithms?

There are 10 letters in the word LOGARITHMS. So, the number of 4-letter words is equal to the number of arrangements of 10 letters, taken 4 at a time, i.e.,. 10P4= 5040.