How many 4 letter words can be formed from mathematics


Asked by admin @ in Math viewed by 314 People


How many words can be formed by taking 4 different letters of the word mathematics?

Answered by admin @



Answer:

2454

Step-by-step explanation:

The four letter word can be formed in the following ways. (all distinct letters),(two letters same of one kind and other two distinct) ,(four letters same of two different kind)


case 1:All distinct letter


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.


case 2:Two letters same of one kind and the other two distinct


The two same letters can be (M,M),(A,A,),(T,T). Choose any one pair among this in 3 ways and two letters from the remaining 7 in 7C2 ways. So total ways of selection is 3*(7C2). Now we can arrange 4 letters of which 2 are of 1 kind in 4!/2!  ways.


So this case gives a total of 3∗(7C2)∗4!/2!  ways=756 ways.


case3:Four letters same of two different kind. Choose any two pair from (M,M),(A,A),(T,T) in 3ways. Now arrange the letters in 4!/(2!∗2!) ways.


So from this case you get a total of 18 ways


So total number of ways =1680+756+18=2454


Hope that was useful


Similar Questions

How many different four letter words can be formed

Asked by admin @ in Math viewed by 541 persons

How many different four letter words can be formed (the words need not be meaningful) using the letters of the word PACIFIC such that the first letter is P and …

How many 4 letter words with or without meaning

Asked by admin @ in Math viewed by 332 persons

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

A letter is chosen at random from the word mathematics

Asked by admin @ in Math viewed by 268 persons

A letter is chosen at random from the word mathematics find the probability that the letter chosen is a vowel and a consonant

The forming of words with letters in the correct order

Asked by admin @ in English viewed by 355 persons

4 letter word lock combinations

Asked by maham237 @ in Mathematics viewed by 300 persons

4 Letter Word Lock* All capital letters. No spaces. Example BLUE

Make 3 4 5 letter words from the word dictionary

Asked by admin @ in English viewed by 305 persons

Make 3 4 5 letter words from the word dictionary

Make 3 4 5 letter words from the word gratification

Asked by admin @ in English viewed by 338 persons

Make 3,4,5 letter word from gratification

What word has 4 letters sometimes 9 but never 5

Asked by admin @ in English viewed by 355 persons

What has 4 letters, sometimes 9, and never 5?

How many uppercase letters in the alphabet have rotational symmetry

Asked by admin @ in Math viewed by 355 persons

List the alphabets having rotational symmetry and reflection symmetry, also list the orders in rotational symmetry as well as reflections symmetry.

6 in word form

Asked by maham237 @ in Mathematics viewed by 266 persons

Write the fraction 5/6 in word form

90523 in word form

Asked by maham237 @ in Mathematics viewed by 269 persons

Write 90,523 in Word form

Indian constitution is made up of how many words

Asked by admin @ in Political Science viewed by 319 persons

Indian Constitution is made up of how many words? A) 40000 B) 60000 C) 80000 D) 120000

Many types of foraminiferans form a symbiotic relationship with _____

Asked by maham237 @ in Biology viewed by 280 persons

12 letters 1 word

Asked by maham237 @ in Mathematics viewed by 312 persons

How many different 12-letter arrangements can be made using the letters in the word indianapolis?

Words with letters lastly

Asked by maham237 @ in English viewed by 328 persons

Read this excerpt from chapter 2 of The Scarlet Letter. Lastly, in lieu of these shifting scenes, came back the rude market-place of the Puritan settlement, with all the townspeople …

Most viewed questions in Math


What is the value of x in the expression

Asked by admin @ in Math viewed by 14999 persons


Shubham is facing south and moves 30 km

Asked by admin @ in Math viewed by 12941 persons


Prachi excellence in mathematics class 7 solutions pdf free download

Asked by admin @ in Math viewed by 11870 persons



Survey of various types of bank accounts icse project

Asked by admin @ in Math viewed by 11458 persons


Oxford new enjoying mathematics class 7 solutions chapter 1

Asked by admin @ in Math viewed by 11440 persons


The town of p is located at point x

Asked by admin @ in Math viewed by 11336 persons



A clock gains 4 minutes after every 4 minutes

Asked by admin @ in Math viewed by 10118 persons


Running a tuck shop or canteen maths project pdf

Asked by admin @ in Math viewed by 9332 persons


Paul is sixteenth from the front of the row

Asked by admin @ in Math viewed by 9320 persons



The average weight of 20 teachers is 80 kg

Asked by admin @ in Math viewed by 7486 persons


The number 567 xy is completely divisible by 30

Asked by admin @ in Math viewed by 7365 persons


In a row of friends tiya occupies fifteenth place

Asked by admin @ in Math viewed by 7172 persons



What would $ mean if fat is coded as

Asked by admin @ in Math viewed by 5246 persons


Consider a 3 digit integer x with distinct digits

Asked by admin @ in Math viewed by 4765 persons


Rahul went to his mother's mother in law

Asked by admin @ in Math viewed by 4154 persons