Question

The number of $5$ lettered word, with or without meaning, which can be formed from letters of word $\text{CHILD}$ when repetition is not allowed are .

Answer 1

Given word is $\text{CHILD}$.

Finding the number of $5$ lettered words is similar to number of ways of filling $5$ vacant places by $5$ letters as shown:


So, first vacant place can be filled in $5$ different ways by any one of the letters $\text{C, H, I, L, D}.$

Since, the repetition of letters is not allowed. Which means no letter can be used more than once.

$\therefore$ Second vacant place can be filled by any of the remaining $4$ letters in $4$ different ways.

Similarly, third, fourth and fifth vacant place can be filled in $3,2$ and $1$ different ways respectively.

Now, by fundamental counting principle the required number of ways is $5\times 4\times 3\times 2\times 1$.

Hence, required number of words formed from word $\text{CHILD}$ is $=5\times 4\times 3\times 2\times 1=120.$