A permutation is an act of arranging the objects or numbers in or… - Vidyadip

Question

A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

How many words, with or without meaning can be made from the letters of the word, $\text{MONDAY,}$ assuming that no letter is repeated if
$(i) 4$ letters are used at a time
$(ii)$ all letters are used at a time

✓

Answer

Total number of letters in word $\text{MONDAY} = 6$
Number of vowels in word $\text{MONDAY} = 2$
$(i)$ Number of letters used $= 4$
$\therefore$ Number of permutations $={ }^6 P_4=\frac{6!}{(6-4)!}$
$=\frac{6!}{2!}=\frac{6 \times 5 \times 4 \times 3 \times 2!}{2!}=360$
$(ii)$ Number of letters used $= 6$
$\therefore$ Number of permutations $={ }^6 P_6$
$=\frac{6!}{0!}$
$=6 \times 5 \times 4 \times 3 \times 2 \times 1$
$=720$

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