How many 7-digit phone numbers can be formed in the first digit cannot be 0, and any digit can be repeated?

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How many 7-digit phone numbers can be formed in the first digit cannot be 0, and any digit can be repeated?

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Answer 1 · 2016-12-13T03:25:31

This is an example of using an advanced counting scheme where we find the answer to be $9$ $9$ million with out having to write them all out!!. Read on...

Explanation:

We consider that each digit is selected independently of the others. This is a consequence of the statement that says digits can be repeated.

The first digit can be any of $1$ $1$ through $9$ $9$ and can be selected in nine different ways. Each remaining digit can then be selected in $10$ $10$ ways, as zero can be used.

Since each digit choice is independent, we just multiply all these choices together:

$N = 9 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 9 million possibilities$ $N = 9 xx 10 xx 10 xx 10 xx 10 xx 10 xx 10 = "9 million possibilities"$

(Shows you why area codes have to come into play.)

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How many 7-digit phone numbers can be formed in the first digit cannot be 0, and any digit can be repeated?

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