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13 Apr 2022, 07:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
43% (02:31) correct
57%
(02:31)
wrong
based on 104
sessions
History
Date
Time
Result
Not Attempted Yet
A is the set of all 4-digit numbers with digits in increasing order and B is the set of all 4-digit numbers with digits in descending order. The difference between the number of elements in sets A and B is
A. 210
B. 126
C. 84
D. 72
E. 26
Are You Up For the Challenge: 700 Level Questions
A. 210
B. 126
C. 84
D. 72
E. 26
Are You Up For the Challenge: 700 Level Questions
13 Apr 2022, 23:22
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Bunuel
Logical conclusion
every decreasing order when reversed will give you an increasing order. ONLY exception is when the decreasing order has 0 in units digit, as reversing will make it a 3-digit number.
Thus number of types 0ABC, where ABC are in increasing order.
Ways ABC can be in increasing order is selecting 3 digits out of remaining 9 digits (1 to 9) = 9C3 = \(\frac{9!}{6!3!}=\frac{9*8*7}{3*2}=84\)
Calculate each way
Ways of arranging digits in decreasing order = choosing 4 digits out of 10 digits. We cannot have 0 in thousands place, and only way 0 can be used in increasing order is left most digit. = 10C4 =\(\frac{10!}{6!4!}=\frac{10*9*8*7}{4*3*2}=210\)
Ways of arranging digits in increasing order = choosing 4 digits out of 9 digits. There is only one way 4 digits can be arranged in increasing/decreasing order. Thus, it becomes selection or combination question = 9C4 =\(\frac{9!}{5!4!}=\frac{9*8*7*6}{4*3*2}=126\)
Difference = 210-126 = 84
C
General Discussion
