How many anagrams can be formed using the letters of the word PROBABILITY?
Ans in the video 9!
Did not understand why shouldnt it be simply 11!/(2!X2!)?

Question

Simran Mehta · Accepted Answer

Hey Megha!Here's a Step-by-step solution:
Total number of letters:The word "PROBABILITY" has 11 letters in total.Repetitions of letters:
The letter "I" appears 2 times.All other letters (P, R, O, B, A, L, T, Y) appear only once.Formula for counting anagrams with repeated letters:If all the letters were unique, the total number of anagrams would be: 11! = 11 &times; 10 &times; 9 &times; 8 &times; 7 &times; 6 &times; 5 &times; 4 &times; 3 &times; 2 &times; 1 = 39,916,800
However, since the letter "I" repeats twice, we need to account for the repeated letters by dividing by the factorial of the number of repeated letters.The formula becomes: (11! / 2!)
This is because there are 2 indistinguishable "I"s.Final calculation:First, calculate 11!: 11! = 39,916,800
Then, divide by 2!= 2
Therefore, the total number of anagrams is: 39,916,800 / 2 = 19,958,400Thus, the total number of anagrams that can be formed using the letters of the word "PROBABILITY" is 19,958,400.

How many anagrams can be formed using the letters of the word PROBABILITY? Ans in the video 9! Did not understand why shouldn't it be simply 11!/(2!X2!)?