Permutations & Combinations
Permutation and Combination
star_batch_jee_advanced_2025
Grade 11
If $p$ is the total number of ways of arranging 36 girls around a table and $q$ is the exponent of 2 in $p$ then the value of $q$ if:
Step-by-Step Solution
Key Concept: The exponent of a prime $p$ in $n!$ is given by Legendre's formula: $\sum_{i=1}^{\infty} \lfloor n/p^i
floor$.
The number of ways to arrange $n$ distinct objects around a circular table is $(n-1)!$ since circular arrangements account for rotational symmetry. For 36 girls, $p = 35!$. To find the exponent of 2 in $35!$, we use Legendre's formula: $q = \lfloor 35/2
floor + \lfloor 35/4
floor + \lfloor 35/8
floor + \lfloor 35/16
floor + \lfloor 35/32
floor = 17 + 8 + 4 + 2 + 1 = 32$. Therefore, $q = 32$.
Correct Answer: [A-p, r, s] [B-p, r, s] [C-q, t] [D-q, t]