Question

A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number can be repeated. You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is ___

If a code is chosen at random, the probability that it has a letter that immediately follows an odd number is ___

If a code is chosen at random, the probability that D is in the code but is not in the first position is ___

ANSWER ALL 3

Answer 1

Answer:

So it can be:

Letter Number Number (and any permutation: Number Letter Number, or Letter Number Number). Three times one case.

For Letter Number Number, there are 4 letters and two numbers. Since numbers cannot be repeated, both of them must be used, because there must be two numbers. So, indeed:

4 * 2 * 1 = 8, but any permutation, so 8 * 3 = 24 is the sample size.

Second question: Must be,

5 Letter 6, so 4 cases: P= 4/24 = 1/6

Third question. May be:

5 D 6, 6 D 5, 5 6 D, or 6 5 D

P = 4/24 =1/6, again!

Step-by-step explanation: