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How many 5 digits telephone numbers can be formed with the dig

Question

How many $5$ digits telephone numbers can be formed with the digits $0, 1, 2, .....9$ , if each number starts with $35$ and no digits appear more than once?

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Michael Discussed

How many

5

digits telephone numbers can be formed with the digits

0, 1, 2, .....9

, if each number starts with

35

and no digits appear more than once?

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

We have to form

5

digit telephone number and the first two places are fixed with

35

, thus we have

10 - 2 = 8

digits for

3

remaining places.

It can be done in

^{8} P_{3}

ways, i.e.,

Total no. of numbers

=^{8} P_{3} = \frac{8 !}{( 8 - 3 ) !} = 8 \times 7 \times 6 = 336

Hence total such telephone numbers are

336

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Question Text	How many $5$ digits telephone numbers can be formed with the digits $0, 1, 2, .....9$ , if each number starts with $35$ and no digits appear more than once?
Answer Type	Text solution:1
Upvotes	150