Factorial : Examples
Example :
Simple Factorial Rules : Click Here
Q1. How many permutations can be formed from the letters of the word “SMILE”?
Soln
5! = 5 × 4 × 3 × 2 × 1 = 120, (All letters distinct)
Ans: 120
Q2. How many permutations can be made using the letters of “GOA”?
Soln
3! = 3 × 2 × 1 = 6, (All letters distinct)
Ans: 6
Medium Factorial Rules : Click Here
Q3. How many different words can be formed from “INDIA”?
Soln
Permutations = 5!/2! = 120/2 = 60, (I repeats 2 times)
Ans: 60
Q4. How many permutations are possible from the letters of “LEVEL”?
Soln
5! / 2! × 2! = 1204 = 30, (L repeats 2 times, E repeats 2 times)
Ans: 30
Tough Factorial Rules : Click Here
Q5. How many permutations can be formed from the word “BALLOON”?
Soln
L repeats 2 times, O repeats 2 times
7! / 2! × 2! = 5040/4 = 1260
Ans: 1260
Q6. How many distinct permutations can be made from “COMMITTEE”?
· M = 2 repeats
· T = 2 repeats
· E = 2 repeats
Soln
9! / 2! × 2! × 2! = 362880/8 = 45360
Ans: 45360
Q1. How many distinct arrangements (words) can be formed using the letters of the word “INDIA”?
a. 120 b. 60 c. 30 d. 24
Ans: b. 60
Explanation: Letters in I,N,D,I,A= 5, Letter I repeats 2 times
Total arrangements = 5!/2! = 120 /2 = 60
Q2. How many different permutations can be formed using all letters of the word “DOCTOR”?
a. 720 b. 360 c. 180 d. 120
Ans: b. 360 Factorial Rules : Click Here
Explanation: Letters in D,O,C,T,O,R = 6, Letter O repeats 2 times
Total arrangements = 6!/2! = 720/2 = 360
Q3. How many distinct arrangements (words) can be made from the letters of “SMILE”?
a. 24 b. 60 c. 120 d. 720
Ans: c. 120
Explanation: All 5 letters are different
5! = 120
Q4. Which word has repeated letters ?
a. SMILE b. DOCTOR c. INDIA d. Both b and c
Ans: d. Both b and c
Explanation:
· DOCTOR → O repeats
· INDIA → I repeats
· SMILE → no repetition
Q5. If all letters are distinct in a word of 5 letters, how many permutations can be formed ?
a. 120 b. 60 c. 720 d. 24