Penelope created a game using a bag of 26 tiles, each with a different letter of the alphabet written on it. She uses a stopwatch to time how fast she can create one 5-letter word from a set of five randomly selected letters. To play this game Penelope randomly draws a letter tile from the bag, writes down the letter and then places the letter tile back in the bag. She does this five times resulting in a set of five randomly chosen letters. Penelope plays the game with each 5‑letter combination only once. If she plans to play the game once for each of the possible 5‑letter combinations that can be randomly selected using the method described, what is the total number of games Penelope will play?

Question

Penelope created a game using a bag of 26 tiles, each with a different letter of the alphabet written on it.  She uses a stopwatch to time how fast she can create one 5-letter word from a set of five randomly selected letters. To play this game Penelope randomly draws a letter tile from the bag, writes down the letter and then places the letter tile back in the bag.  She does this five times resulting in a set of five randomly chosen letters.  Penelope plays the game with each 5‑letter combination only once. If she plans to play the game once for each of the possible 5‑letter combinations that can be randomly selected using the method described, what is the total number of games Penelope will play?

vnvb · Answer

98

Explain Bot · Answer

To find the total number of games Penelope will play, we need to determine the number of possible 5-letter combinations that can be randomly selected using the method described. Since Penelope randomly draws a letter tile from the bag and then places it back before drawing the next one, this is an example of sampling with replacement. In such a sampling method, each draw is independent of the previous ones and all the letters have an equal chance of being selected again. To calculate the number of possible combinations, we can use the concept of permutations with repetition. In this case, we have 26 options for each of the 5 positions in the combination (since there are 26 different letters in the bag). Therefore, the total number of games Penelope will play can be found using the formula: Number of games = 26 × 26 × 26 × 26 × 26 = 26^5 = 11,881,376 So, Penelope will need to play a total of 11,881,376 games to cover all the possible 5-letter combinations.