A bag contains one tile for each letter of the word PANDA.

Question

If you selected a permutation of these letters at random, what is the probability that they would spell the word panda? Hint: Note that there is a repeated letter.

Answer 1

At first, there are five tiles, but only one is a P, so your chance of drawing the P is 1 in 5, or 1/5.

Now, there are four tiles, and two of them are an A, so your chance of drawing an A is 2 in 4, or 1/2.

Now, there are three tiles, but only one is an N, so your chance of drawing an N is 1 in 3, or 1/3.

Now, there are two tiles, but only one is a D, so your chance of drawing a D is 1 in 2, or 1/2.

Finally, there is only one tile left, so your chance of drawing an A is 1 in 1, or 1.

To calculate the chance multiple events happening together, simply multiply the individual chances of everything that you want to happen at the same time.

1/5 * 1/2 * 1/3 * 1/2 * 1 = 1/60 or 1 in 60.