Question

Find the number of four-letter words that can be formed using the letters of the word PISTON, in which at least one letter is repeated.

Answer 1

In the given question first we have to count the total number of alphabets is the given word PISTON. Then we have to find the number of four-letter words that can be formed with repetition, Number of four-letter words that can be formed without repetition. Then we can calculate the number of four-letter words that can be formed at least with one repetition.

Complete step-by-step solution:
From the given question we can write that:
The number of distinct alphabets in the word PISTON is 6.
Now we have to make several four-letter words
The number of four-letter words that can be formed with repetition will be,
$\Rightarrow 6 \times 6 \times 6 \times 6 = 1296$
Because the total number of letters is six.
Now again according to the question:
The number of four-letter words that can be formed without repetition will be,
$\Rightarrow 6 \times 5 \times 4 \times 3 = 360$
Now, the number of four-letter words that can be formed at least with one repetition will be
$\Rightarrow$ (Number of four-letter words that can be formed with repetition) – (Number of four-letter words that can be formed without repetition)
Substitute the value,
$\Rightarrow 1296 - 360 = 936$

Hence, the number of four-letter words that can be formed with the letters in the word PISTON with at least one letter repeated is 936.

Note: In the given question we have to remember the word formula can be formed with one repetition because this formula is used in the given problem i.e., Number of four-letter words that can be formed at least with one repetition = (Number of four-letter words that can be formed with repetition)-(Number of four-letter words that can be formed without repetition).