Marissa is choosing a four-digit pin for her atm card. the first digit must be a digit from 1 through 9. for the other three digits, she can choose any combination of digits 0 through 9, but may not repeat a digit. which shows part of the sample space for marissa’s pin?

0123, 0456, 0789
1012, 1033, 1004
2345, 2034, 2134
3200, 4200, 5200

2345, 2034, 2134

Step-by-step explanation:

We know that the first digit out of the four-digit PIN must be between 1 to 9. Also, other three digits must be any combination of 0 to 9 with no repetition.

Now according to options:

A. 0123, 0456, 0789: the first digit is 0, which is not possible.

B. 1012,1033,1004: there is repetition in the last three digits of the 4-digit PIN, which is again not possible.

D. 3200, 4200, 5200: same as option B there is a repetition in the digits, which is not possible.

Hence, option C. 2345, 2034, 2134 is correct.

do you have a picture of the table

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb