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?
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
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