Table of Contents

- 1 How many word can be formed by taking 4 letters at a time out of the letters of the word mathematics?
- 2 How many 4 letter words can be formed using the letters of the word college if each letter has to be distinct?
- 3 How many 4 letter words can be formed using the letter of the word mathematics?
- 4 How many ways we can arrange 4 letters from Professor?
- 5 How many 4 letter words can be formed using the letters of the word proportion?
- 6 How many words can be formed by taking 4 letters of the word Moradabad?
- 7 How many ways can 4 letters be arranged?
- 8 How many ways word can be arranged?
- 9 How many ways to arrange letters of a word?
- 10 How many pairs of letters can be chosen by 3c2?

## How many word can be formed by taking 4 letters at a time out of the letters of the word mathematics?

Step-by-step explanation: We have 8 distinct letters( M,A,T,H,E,I,C,S). We choose any 4 from this and then arrange it in 8P4 ways=1680 ways.

## How many 4 letter words can be formed using the letters of the word college if each letter has to be distinct?

∴ 840 four-letter words can be formed when the repetition of letters is not allowed.

**How many different words can be formed by taking 4 letters from the word arrange without replacement?**

Using properties of factorial, we can write the numerator as, ⇒10P4=10×9×8×7×6! 6! Therefore, the number of four-letter words that can be formed is 5040.

### How many 4 letter words can be formed using the letter of the word mathematics?

Therefore, the number of ways in which four letters of the word MATHEMATICS can be arranged is 2454.

### How many ways we can arrange 4 letters from Professor?

Now we can arrange 4 letters of which 2 are of 1 kind in ways. So this case gives a total of ways=756 ways.

**How many different words of 4 letters can be formed with the letters of the word examination?**

Therefore total of 2454 four letter words can we formed from the letters of the word “EXAMINATION”.

#### How many 4 letter words can be formed using the letters of the word proportion?

Now, each combination can be arranged in 4! 3! . Hence, 758 ways of 4 letter words can be arranged by the letters of the word PROPORTION.

#### How many words can be formed by taking 4 letters of the word Moradabad?

626 words

626 words can be formed by taking $4$ letters at a time from the letters of the word ‘MORADABAD.

**How many 4 letter words can be formed from the letters of the word answer?**

Hence, 360 ways of 4 letter words can be formed from the letters of the word ‘ANSWER’ and 120 ways of 4 letter words start with vowels.

## How many ways can 4 letters be arranged?

24

The answer is 4! = 24. The first space can be filled by any one of the four letters.

## How many ways word can be arranged?

=n×(n−1)×(n−2)×…… ×3×2×1. Therefore, we can arrange the letters in the word ‘FACTOR’ in 720 ways. Thus, this is the required answer.

**How many ways are there of selecting 4 letters?**

To find: No. of ways of selecting 4 letters. Case I : When all are different letters. => No of ways = 4C4 = 1 ways. Case II : When 3 alike 1 different Here it is to be noted that for 3 letters to be alike, only E is eligible since it is the only letter occurring 3 times. Then remaining single letter is to be selected from 3 types (D,G & R).

### How many ways to arrange letters of a word?

Number of Ways to Arrance ‘n’ Letters of a Word ‘n’ Letters Words Ways to Arrange 7 Letters Word 5,040 Distinct Ways 8 Letters Word 40,320 Distinct Ways 9 Letters Word 362,880 Distinct Ways 10 Letters Word 3,628,800 Distinct Ways

### How many pairs of letters can be chosen by 3c2?

Two pairs can be chosen by 3C2 3C2 groups of 4 letters each. There are 4 letters of which 2 alike of one kind and two alike of other kind in each group. That can be arranged by 4!/2! × 1/2!

**How many different ways can 3 letters be alike?**

=> No of ways = 4C4 = 1 ways. Case II : When 3 alike 1 different Here it is to be noted that for 3 letters to be alike, only E is eligible since it is the only letter occurring 3 times. Then remaining single letter is to be selected from 3 types (D,G & R).