Q79·CSAT · Prelims 2022
Counting two-digit decimal combinations with non-zero constraints
NumericalNumber SystemFactual single● Easy
Question
What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?
Options
aAnswer
72
b
81
c
90
d
100
Explanation
The problem asks for permutations to fill the string template `0.XY`.
The conditions specify that X and Y are non-zero digits and distinct.
The available pool of digits is \{1, 2, 3, 4, 5, 6, 7, 8, 9\}.
Calculate the options for each slot:
Slot X: Can be any of the 9 available digits. (9 choices)
Slot Y: Must be non-zero and cannot be whatever digit was just assigned to X. (9 - 1 = 8 choices)
Multiply independent probabilities: 9 × 8 = 72 numbers.
For non-zero distinct permutations, simply execute descending factorials matching the slot count against the baseline of 9 (9 × 8 × 7 \dots).
Answer: (a).
Question details
Year
2022
Paper
CSAT
Question
Q79
Section
Numerical Ability
Sub-topic
Number System
Type
Factual single
Difficulty
Easy
Source hint
Form 0.XY
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