Name: Problem on Properties of Combination
Uploaded: 2019-07-19
Duration: 3 min 49 s
Description: A combination is a selection of items from a collection, such that the order of selection does not matter. Let's learn how to apply an appropriate property o...

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?

Accepted Answer

Given that, The digits from $0$ to $9$ is to be used to form $5$ -digit telephone numbers so that each number always start with $67$ .

Here, the number of digits $= 10$ and the number of places $= 5$ .

Let the arrangement is given by, $67$ .

So, there will be as many phone numbers as there are ways of filling $3$ vacant places by the digits $0, 1, 2, 3, 4, 5, 8, 9$ as the other two digits are already used.

Thus, the ones place can be filled by any of the digits from $0 to 9$ , except digits $6$ and $7$ .

Thus, the units place can be filled in $8$ different ways following which, the tens place can be filled in by any of the remaining $7$ digits in $7$ different ways, and the hundreds place can be filled in by any of the remaining $6$ digits in $6$ different ways.

Therefore, by multiplication principle, we have $8 \times 7 \times 6 = 336$

Hence, $336$ telephone numbers can be constructed.

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?

Important Questions on Permutations and Combinations

Learn and Prepare for any exam you want !

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?

Important Questions on Permutations and Combinations

Learn and Prepare for any exam you want !

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?