The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.
Correct Answer: 576
Solution and Explanation
Sum of all given numbers = 31
Difference between odd and even positions must be 0, 11 or 22, but 0 and 22 are not possible.
Therefore , Only difference 11 is possible
This is possible only when either 1, 2, 3, 4 is filled in odd position in some order and remaining in other
order. Similar arrangements of 2, 3, 5 or 7, 2, 1 or 4, 5, 1 at even positions.
∴ Total possible arrangements = (4! × 3!) × 4
= 576
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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.