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12 Mar 2021, 03:15
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:13) correct
28%
(02:27)
wrong
based on 179
sessions
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Ten different letters of an alphabet are given, words with 4 letters are formed from these given letter. Then what is the number of words which have at least one letter repeated ?
(A) 10000
(B) 9900
(C) 9000
(D) 5040
(E) 4960
(A) 10000
(B) 9900
(C) 9000
(D) 5040
(E) 4960
18 Mar 2021, 06:35
Kudos
Bookmarks
If we pick 4 letters from 10 different letters with repetition, the number of words will be 10*10*10*10 = 10,000
If we pick 4 letters from 10 different letters without repetition, the number of words will be 10*9*8*7 = 5,040
If we exclude words without repetition from words with repetition, we will get the number of words that have at least one word repeated.
10,000 - 5,040 = 4960. (OPTION: E IMO)
If we pick 4 letters from 10 different letters without repetition, the number of words will be 10*9*8*7 = 5,040
If we exclude words without repetition from words with repetition, we will get the number of words that have at least one word repeated.
10,000 - 5,040 = 4960. (OPTION: E IMO)
29 Mar 2021, 11:10
Kudos
Bookmarks
Bunuel
Ten different letters of an alphabet are given, words with 4 letters are formed from these given letter. Then what is the number of words which have at least one letter repeated ?
(A) 10000
(B) 9900
(C) 9000
(D) 5040
(E) 4960
Solution:(A) 10000
(B) 9900
(C) 9000
(D) 5040
(E) 4960
The total number of 4-letter words that can be formed is 10 x 10 x 10 x 10 = 10,000. The total number of 4-letter words without any repeating letters that can be formed is 10 x 9 x 8 x 7 = 5,040. Therefore, the total number of 4-letter words (with at least one repeating letter) that can be formed is 10,000 - 5,040 = 4,960.
Answer: E
