Five cards are lettered A B C D E.Three cards are chosen at random, one after the other, without replacement and are placed in the order.what is the probability that the cards spell the word BED

There are no permutations in probability

To calculate the probability of drawing the cards in the specific order to spell the word "BED," we need to calculate the number of favorable outcomes and the total number of possible outcomes.

First, let's calculate the total number of possible outcomes:

There are five cards in total, and we are drawing three cards without replacement. Therefore, the total number of possible outcomes is given by the permutation formula:

Total number of outcomes = P(5,3) = 5! / (5-3)! = 5! / 2! = 5 * 4 * 3 = 60

Now, let's determine the number of favorable outcomes:

We want to spell the word "BED" in that specific order. We can see that the card "B" must be drawn first, followed by "E," and then "D."

The number of ways to draw the card "B" first is 1, as there is only one card with the letter "B."
After drawing "B," there are four remaining cards in the deck, so the number of ways to draw the card "E" is 1.
Finally, after drawing "B" and "E," there are three remaining cards, so the number of ways to draw the card "D" is 1 as well.

Therefore, the number of favorable outcomes is 1 * 1 * 1 = 1.

Now we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 60

The probability of drawing the cards in the specific order to spell the word "BED" is 1/60.

To find the probability that the cards spell the word "BED" in the given order, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:
Since we are choosing 3 cards without replacement, the total number of possible outcomes can be calculated as the number of ways to arrange 5 cards taken 3 at a time. This can be expressed as 5P3.

Number of favorable outcomes:
To spell the word "BED" in the given order, we need to choose the card labeled "B" first, then "E," and finally "D." The number of favorable outcomes is 1 since there is only one way to arrange these specific cards.

Calculating the probability:
The probability P of an event can be defined as the ratio of favorable outcomes to total outcomes: P = Number of favorable outcomes / Total number of outcomes.

So, let's calculate the probability:

Total number of outcomes: 5P3 = (5!/2!) = 5*4*3 = 60
Number of favorable outcomes = 1

Probability of spelling "BED" in order: P = 1/60

Therefore, the probability that the cards spell the word "BED" in the given order is 1/60.

doing selection without replacement, the chance is

1/5 * 1/4 * 1/3 = 1/60

or, since there are 5P3 = 60 permutations of 3 of the 5 letters, and only one of them spells BED, the chance is 1/60