The number of four-letter words that can be f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The word $BARRACK$ contains $7$ letters: $A, A, R, R, B, C, K$. Case $I$: All four letters are different. We choose $4$ letters from ${A, R, B, C,

Vedclass · Accepted Answer

$270$

Vedclass · Answer

(C) The word $BARRACK$ contains $7$ letters: $A, A, R, R, B, C, K$. Case $I$: All four letters are different. We choose $4$ letters from ${A, R, B, C, K}$. Number of ways $= {}^{5}C_{4} 	imes 4! = 5 	imes 24 = 120$. Case $II$: Two letters are the same $(R, R)$ and two are different. We choose $2$ letters from ${A, B, C, K}$. Number of ways $= {}^{4}C_{2} 	imes \frac{4!}{2!} = 6 	imes 12 = 72$. Case $III$: Two letters are the same $(A, A)$ and two are different. We choose $2$ letters from ${R, B, C, K}$. Number of ways $= {}^{4}C_{2} 	imes \frac{4!}{2!} = 6 	imes 12 = 72$. Case $IV$: Two letters are $A, A$ and two are $R, R$. Number of ways $= \frac{4!}{2!2!} = 6$. Total number of words $= 120 + 72 + 72 + 6 = 270$.

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is:

Similar Questions

Which of the following statements is true?

Identify $A$ and $B$ in the following reactions:

In any $\triangle ABC$,$r_1 r_2 + r_2 r_3 + r_3 r_1$ is equal to

Mosses and ferns are found in moist and shady places because both

Fluorine is more electronegative than either boron or phosphorus. What conclusion can be drawn from the fact that $BF_3$ has no dipole moment but $PF_3$ does?

Vedclass Test Series

Exam Paper Generator

Online Exam Module