Question

HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:

Answer 1

Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:

a) 900,000.

b) 78,125.

c) 10,000.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:

$n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1$

Hence the number is:

N = 9 x 10^5 = 900,000.

For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:

$n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5$

Hence the number is:

N = 5^7 = 78,125.

For item c, if the first 3 digits are 277, the parameters are:

$n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10$

Hence the number is:

N = 10^4 = 10,000.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

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