Question

The number of four letter words that can be formed using the letters of the word barrack is

Answer 1

rack;bark I think only 2

Answer 2

Answer:

The number of four letter words that can be formed using the letters of the word barrack is 270

Step-by-step explanation:

In the word BARRACK,

Different letters = 2A, 2R, 1B, 1C, 1K

There are three cases that can occur when we form four letter word

Case 1 :

When all the letters are different

_ _ _ _

In that case,

For the four position we have ⁵C₄ choices

And all these letters can arrange among themselves in 4 ! ways

So,

Number of words that can be formed in this case = ⁵C₄ * 4! = 120

Case 2 :

When two alike letters are of one kind and two alike letters of other kind

AARR = $\frac{4!}{2!*2!}$ = 6

Case 3 :

When two alike letters are of one kind and other two letters are different

So,

for two alike of one kind = ²C₁

two letters of different kind = ⁴C₂

They can arrange themselves in $\frac{4!}{2!}$ ways

So,

Number of words that can be formed = ²C₁ * ⁴C₂ *  $\frac{4!}{2!}$ ways

= 2 * 6 * 12 = 144

Therefore,

Total number of four letter word = 120 + 6 + 144 = 270

Hence,

The number of four letter words that can be formed using the letters of the word barrack is 270