Question

Erin has 4 cards, one with the letter A, one with the letter B, one with the letter C, and one with the letter D. She places the cards in a row in random order.

What is the probability that either the words BAD or CAB will appear as part of the row?

Answer 1

The probability would be 16.7%

Answer 2

P = 1/6

Explanation:

We have 4 places where we can put the cards.

Let's count the number of possible outcomes for each place.

In the first place, we can put one of 4 cards.

in the second place, we can put one of 3 cards (because there is already one card in the first place)

In the third place, we can put one of 2 cards

In the last place, we can put one of one cards.

The total number of different combinations is the product between the number of options for each place, then we have:

C = 4*3*2*1 = 24

Now we need to count the number of combinations such that the words BAD or CAB appear.

Those are:

BADC

CBAD

CABD

DCAB

4 outcomes out of 24.

Then the probability will be equal to the quotient between the number of outcomes where one of these words appears (4) and the total number of possible outcomes (24)

The probability is:

P = 4/24 = 1/6