An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :
- 72 (7!)
- 18 (7!)
- 40 (7!)
- 36 (7!)
The Correct Option is D
Solution and Explanation
(i) Total no formed by 1,2,3,4,5, 6,7,8 = 81
(ii) Total no formed by 0,2,3,4,5,6,7,9 = 7$\times$7!
(iii) Total no formed by 1,0,3,4,5,6,9,8 = 7$\times$7!
(iv) Total no formed by 1,2,0,4,5,9,7,8 = 7$\times$7!
(v) Total no formed by 1,2,3,0,5,6,7,8 = 7$\times$7!
8! + 28 $\times$ 7 !
= 36 $\times$ 7 !
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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.