Question:
How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?
How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?
Updated On: Apr 18, 2024
- 336
- 337
- 335
- 338
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The Correct Option is A
Solution and Explanation
Since, telephone number start with 67 , so two digits is already fixed. Now, we have to arrangement of three digits from remaining eight digits (i.e., $0,1,2,3,4,5,8,9$)
$={ }^{8} P_{3}$ ways $=\frac{8 !}{5 !}$
$=8 \times 7 \times 6$
$=336$ ways
$={ }^{8} P_{3}$ ways $=\frac{8 !}{5 !}$
$=8 \times 7 \times 6$
$=336$ ways
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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.