Permutations & Combinations
Permutation and Combination
star_batch_jee_advanced_2025
Grade None
Question:
Which of the following statements are correct?
Number of 6 letter words that can be formed using letters of the word "CENTRIFUGAL" if each word must contain all the vowels is $3 \times 7$
There are 15 balls of which some are white and the rest black. If the number of ways in which the balls can be arranged in row, is maximum then the number of white balls must equal to 7 or 8. Assume balls of the same colour are alike
There are 12 things, 5 alike of one kind, 4 alike and 5 alike and of another kind and the rest are all different. The total number of combinations is 240
Number of selections that can be made of 6 letters from the word "COMMITTEE" is 35
Step-by-Step Solution
Key Concept: Simplify compound expressions by recognizing common bases and perfect power patterns before computing.
We solve $N = \frac{(7+18)^6}{(3+2)^6} - 1 = \frac{25^6}{5^6} - 1 = 5^6 - 1$. Computing $5^6 = 15625$, we get $N = 15624$.
Correct Answer: 1,2,3,4