How many different selections of four letters from the 12 letters of the word REFRIGERATOR contain no Rs and two Es?
I would start by breaking this down.
How many unique selections of four letters are there?
How many contain no R's?
How many contain exactly 2 E's?
Can I do it directly using 9/2! * 4!/4!
Let me know how you would do it?
https://math.stackexchange.com/questions/2872662/permutation-selection-of-4-letters-from-12
To find the number of different selections of four letters from the 12 letters of the word "REFRIGERATOR" that contain no Rs and two Es, we can use the concept of combinations.
Here's how you can calculate it step by step:
Step 1: Count the total number of Es in the word "REFRIGERATOR". In this case, there are three Es.
Step 2: Since we want to select two Es, we need to choose two out of the three Es. We can do this by using combinations. The number of ways to choose two items from three is denoted as "3C2" and can be calculated using the formula: 3C2 = 3! / (2! * (3 - 2)!) = 3.
Step 3: Now, we need to find the remaining two letters from the remaining 9 letters (removing all the Rs and the two selected Es). So, we have 9 remaining letters to choose from.
Step 4: Since order doesn't matter in this problem, we can use combinations again. We need to choose two letters from the remaining 9 letters. This can be calculated as 9C2 = 9! / (2! * (9 - 2)!) = 36.
Step 5: Finally, multiply the number of selections from Step 2 (3) by the number of selections from Step 4 (36) to get the total number of different selections of four letters from the word "REFRIGERATOR" that contain no Rs and two Es.
3 * 36 = 108
Therefore, there are 108 different selections of four letters from the 12 letters of the word "REFRIGERATOR" that contain no Rs and two Es.