Ahmad is choosing a password to access his teacher’s web page. He must choose a capital letter and three nonrepeating digits from 0 through 9. The letter can be in any position in the password. Which shows part of the sample space for Ahmad’s password?
A135, 135A, 1A35, 13A5
A135, 135A, 1A35, 13A5
A113, A123, A133, A143
0A23, 0a23,02A3, 02a3
1234, 5678, 0246, 1357
A135, 135A, 1A35, 13A5. I hope this answer helps!
What are your choices?
To determine the sample space for Ahmad's password, we need to consider all possible combinations of a capital letter and three non-repeating digits from 0 through 9.
There are 26 possible capital letters (A-Z) and 10 possible digits (0-9). Since the digits must be non-repeating, we can use the concept of combinations.
To find the number of combinations, we use the equation: nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items chosen at a time.
In this case, we have 26 choices for the capital letter (n = 26) and need to choose 3 non-repeating digits (r = 3) from 10 possible digits (n = 10).
Therefore, the total number of possible combinations is given by:
26C1 * 10C3 = (26! / (1!(26-1)!)) * (10! / (3!(10-3)!))
= 26 * (10! / (1! * 9!)) * (10 * 9 * 8) / (3 * 2 * 1)
= 26 * 120 * 10
= 31,200
So, there are 31,200 possible combinations for Ahmad's password.