Question

How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

Column I		Column II
A	4 letters are used at a time	1	720
B	All letters are used at a time	2	240
C	All letters are used but the first is a vowel	3	360

Match the statements in Column I with Column II and choose the correct option from the codes given below.

• A. A - (1), B -(2), C - (3)
• B. A - (3), B -(1), C - (2)
• C. A - (2), B -(1), C - (3)
• D. A - (3), B -(2), C - (1)

Answer 1

Answer: (B)

A. Number of words using 4 letters out of 6 letters
$={}^6{P}_4=\frac{6!}{2!}=6\times 5\times 4\times 3$
$=360$
B. Number of words using all letters $={}^6{P}_6=6$ !
$=720$
C. Number of words starting with vowel
$=$ Number of ways of choosing first letter ( out of $O$ and
A) $\times$ Number of ways of arranging 5 alphabets
$=2\times 5!=2\times 120=240$