The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to _______.
Correct Answer: 1086
Solution and Explanation
The correct answer is 1086
Let pqrs is 4-digit number.
So , first 3-digit pqr should be divisible by 's'
If s=1 , then numbers = 9×10×10 = 900
If s=2 , then numbers = 4×5×5 = 100
If s=3, then numbers = 3×4×4 = 48
If s=4, then numbers = 2×3×3 = 18
If s=5, then numbers = 1×2×2 = 4 numbers
If s=6,7,8 and 9 then , numbers = 4×4 = 16
∴ Total 4 digit Number = 900 + 100 + 48 + 18 + 4 + 16 = 1086
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.