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01 Mar 2021, 05:46
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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:
5%
(low)
Question Stats:
88% (00:42) correct
12%
(00:51)
wrong
based on 78
sessions
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How many 5-digit numbers can be formed from the digits 2, 3, 5, 6, 8, 9 if no digit can be used more than once in a number ?
A. 120
B. 240
C. 360
D. 720
E. 1080
A. 120
B. 240
C. 360
D. 720
E. 1080
01 Mar 2021, 06:13
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Basically the question is asking how many 5 digit numbers can be formed without repetition.
If we do by the box method, then the 1st place can be filled in 6 ways, second in 5, 3rd in 4 4th in 3 and the last in 2 ways.
Total number of ways = 6 * 5 * 4 * 3 * 2 = 720
In terms of permutations, we need to arrange 5 digit out of 6 = 6P5 = 6! / (6 - 5)! = 720 ways
In terms of combinations, first choose 5 numbers out of 6 in 6C5 ways and then arrange these 5 digits in 5! ways.
Total arrangements = 6C5 * 5! = 6 * 5! = 720
Option D
Arun Kumar
If we do by the box method, then the 1st place can be filled in 6 ways, second in 5, 3rd in 4 4th in 3 and the last in 2 ways.
Total number of ways = 6 * 5 * 4 * 3 * 2 = 720
In terms of permutations, we need to arrange 5 digit out of 6 = 6P5 = 6! / (6 - 5)! = 720 ways
In terms of combinations, first choose 5 numbers out of 6 in 6C5 ways and then arrange these 5 digits in 5! ways.
Total arrangements = 6C5 * 5! = 6 * 5! = 720
Option D
Arun Kumar
01 Mar 2021, 07:28
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Bunuel
We have 5 empty places like this
- - - - -
We have 6 digits to use and the digit can NOT be repeated
Method-1
So we can fill the first place in 6 ways
6 - - - -
So we can fill the Second place in 5 ways (can not use the used digit at first place)
6 * 5 - - -
So we can fill the Third place in 4 ways (can not use the used digits at previous places)
6 * 5 * 4 - -
So we can fill the Forth place in 4 ways (can not use the used digits at previous places)
6 * 5 * 4 * 3 -
So we can fill the Fifth place in 4 ways (can not use the used digits at previous places)
6 * 5 * 4 * 3 * 2
So total numbers =
720
ANswer: Option D
Method-2
Step-1: Select 5 out of 6 digits that need to be used to make a five digit number in
\(^6C_5\)
waysStep-2: Arrange those selected digits at 5 places in
5!
waysTotal Such numbers =
\(^6C_5*5! = 720\)
ANswer: Option D
