Question

20 different letters of alphabet are given. words with six letters are formed from these given letters. find the number of words which have at least one letter repeated?

Answer 1

Answer:

Number of words which have at least one letter repeated = 36092800

Step-by-step explanation:

Number of letters given to form the words = 20

Number of letter words to be formed = 6

Now, we need to find the number of words which have at least one letter repeated.

$\text{So, Total number of words = }20^6=64000000$

[tex]\text{Also, Total number of words in which no letter is repeated = }_6^{20} \txterm{P}=27907200 [/tex]

Now, Number of words which have at least one letter repeated = Total number of words - number of words in which no letter is repeated

= 64000000 - 27907200

= 36092800

Hence, Number of words which have at least one letter repeated = 36092800