How many words can be formed from the letters of the word ‘SUNDAY’? How many of these begin with D?
There are 6 letters in the word SUNDAY.
Different words formed using 6 letters of the word SUNDAY is $P(6,6)$
Formula:
Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is
$P(n, r)=n ! /(n-r) !$
Therefore, a permutation of 6 different objects in 6 places is
$P(6,6)=\frac{6 !}{(6-6) !}=\frac{6 !}{0 !}=\frac{720}{1}=720$
720 words can be formed using letters of the word SUNDAY.
When a word begins with $D$.
Its position is fixed, i.e. the first position.
Now rest 5 letters are to be arranged in 5 places.
Formula:
Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is
$P(n, r)=n ! /(n-r) !$
Therefore, a permutation of 5 different objects in 5 places is
$P(5,5)=\frac{5 !}{(5-5) !}=\frac{5 !}{0 !}=\frac{\frac{120}{1}}{1}=120$
Therefore, the total number of words starting with D are 120.