1. Tardigrade
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  3. Mathematics
  4. 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.

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Q. 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.

Permutations and Combinations

Solution:

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
$=2 \times 5 !=2 \times 120=240$