Answer
The answer = 5,184,000,000
There are 5,184,000,000 possible phone numbers.
Step-by-step explanation
The question told us that telephone numbers are in the form NYZ-ABC-XXXX, then proceeds to give us the restrictions on some of the positions available.
- N can only be numbers: 2-9;
- Y can only be numbers 0-7
- and A&C cannot be 2
We are then told to calculate the number of phone numbers possible.
This question is a special type of permutation and combination.
To solve it, it will be a multiplication of the possible numbers that can take up each position.
N, can only be numbers 2 to 9. Number of possible digits = 8
Y, can only be numbers 0 to 7. Number of possible digits = 8
Z, no restriction, can have numbers 0 to 9. Number of possible digits = 10
A, number cannot be 2. Number of possible digits = 9
B, no restriction, can have numbers 0 to 9. Number of possible digits = 10
C, number cannot be 2. Number of possible digits = 9
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
Total number of possible phone numbers
= 8 × 8 × 10 × 9 × 10 × 9 × 10 × 10 × 10 × 10
= 5,184,000,000
Hope this Helps!!!