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16 May 2018, 04:49
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (00:55) correct
28%
(00:57)
wrong
based on 218
sessions
History
Date
Time
Result
Not Attempted Yet
How many five-digit numbers can be formed using the digits 5, 6, 7, 8, 9, 0 if no digits can be repeated
(A) 64
(B) 120
(C) 240
(D) 600
(E) 720
(A) 64
(B) 120
(C) 240
(D) 600
(E) 720
16 May 2018, 04:58
Kudos
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Solution
Given:
• 5-digit numbers needs to be formed using the digits 5, 6, 7, 8, 9, and 0
• Repetition of digits not allowed
To find:
• How many such numbers can be formed
Approach and Working:
We can find the possible cases by taking the number of options for each place.
Considering the left-most digit as the 1st digit and right-most digit as the 5th or last digit,
• No of ways 1st place can be filled = 5 [except 0]
• No of ways 2nd place can be filled = 5 [all number except the 1st digit]
• No of ways 3rd place can be filled = 4 [all number except the 1st two digits]
• No of ways 4th place can be filled = 3 [all number except the 1st three digits]
• No of ways 5th place can be filled = 2 [all number except the 1st four digits]
Hence the total number of possible cases = \(5*5*4*3*2\) = 600
Hence, the correct answer is option D.
Answer: D
18 May 2018, 11:17
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Bunuel
Since the first digit can’t be 0, there are 5 choices for the first digit. Since the second digit can’t be repeated (but it can be 0), there are also 5 choices for the second digit. There are 4 choices for the third digit, 3 for the fourth and 2 for the fifth. Therefore, there are 5 x 5 x 4 x 3 x 2 = 600 five-digit numbers possible.
Answer: D
