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An alarm system has a keypad with 6 buttons. How many possible 4-button alarm codes are there if each button can only be used once?

User Moini
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Final answer:

The total number of possible 4-button alarm codes you can create from a keypad with 6 different buttons is 360; this calculation is based on permutations without repetition.

Step-by-step explanation:

The student wants to know how many different 4-button alarm codes can be created from a keypad with 6 buttons, with each button being used only once. This is a problem of permutations because the order in which the buttons are pressed matters. We calculate this using the formula for permutations without repetition, which is given as P(n, r) = n! / (n-r)! where 'n' is the total number of items to choose from, and 'r' is the number of items to choose.

The number of possible 4-button alarm codes can be found using the concept of permutations. Since each button can only be used once, we need to find the number of ways to arrange the 4 buttons from the 6 available options. This can be calculated using the formula for permutation.

Permutation formula: nPr = n! / (n - r)!

In this case, n = 6 (number of available buttons) and r = 4 (number of buttons to be arranged).

Plugging in the values, we get:

6P4 = 6! / (6 - 4)! = 6! / 2! = (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1) = 6 x 5 x 4 x 3 = 360.

Therefore, there are 360 possible 4-button alarm codes.

User Tuslareb
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