Probability of choosing two letters from the word LIME

To find the probability of choosing the letters L and M from the word LIME, we need to first determine the total number of possible outcomes and the favorable outcomes.

Step 1: Total number of possible outcomes
The word LIME has 4 letters. To find the total number of possible outcomes, we need to choose 2 letters from these 4 letters. This can be calculated using the combination formula:

nCr = n! / (r!(n-r)!)

In this case, n = 4 (total number of letters) and r = 2 (number of letters to be chosen).

4C2 = 4! / (2!(4-2)!) = 4! / (2!2!) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6

Therefore, the total number of possible outcomes is 6.

Step 2: Number of favorable outcomes
To find the number of favorable outcomes, we need to determine the number of ways we can choose the letters L and M from the word LIME.

The letter L appears only once in the word LIME, so we have only one option for choosing L.

The letter M also appears only once in the word LIME, so we have only one option for choosing M.

Therefore, the number of favorable outcomes is 1.

Step 3: Calculating the probability
The probability of an event is given by the formula:

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

In this case, the number of favorable outcomes is 1 and the total number of possible outcomes is 6.

Therefore, the probability of choosing the letters L and M from the word LIME is:

Probability = 1 / 6 = 0.1667 (rounded to four decimal places) or 16.67%