Question

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

Answer 1

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