37.6k views
4 votes
how many different four digit alarm codes can be formed for a house alarm? The first digit must be 7 or 9, and all the other digits can be any number and repetition is not allowed.

1 Answer

3 votes

Final answer:

There are 1008 different four-digit alarm codes that can be formed for a house alarm.

Step-by-step explanation:

The total number of different four-digit alarm codes that can be formed for a house alarm can be found by considering the restrictions given in the question. Since the first digit must be 7 or 9, there are 2 options for the first digit. For the remaining three digits, any number from 0 to 9 can be chosen, excluding the already chosen digits. Therefore, there are 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit.

Using the multiplication principle, the total number of four-digit alarm codes is calculated as:

2 * 9 * 8 * 7 = 1008.

Therefore, there are 1008 different four-digit alarm codes that can be formed for the house alarm.

User Michoel
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories