QJEEM24Ma1b29: JEE Main 2024 Mathematics - Class 11 JEEM24Ma1b29 Solution: Let α = ( 4 ! ) ! ( 4 ! ) 3 ! and β = ( 5 ! ) ! ( 5 ! ) 4 ! .…

Question

Verified Solution • 2025–26 Session moderate

Let $α = \frac{(4!)!}{(4!)^{3!}}$ and $β = \frac{(5!)!}{(5!)^{4!}}$ . Then :

Accepted Answer

$\begin{aligned} α = \frac{(4!)!}{(4!)^{3!}}, β = \frac{(5!)!}{(5!)^{4!}} \\ α = \frac{(24)!}{(4!)^{6}}, β = \frac{(120)!}{(5!)^{24}} \end{aligned}$

Let 24 distinct objects are divided into 6 groups of 4 objects in each group.

No. of ways of formation of group $= \frac{24!}{(4!)^{6} .6!} \in N$

Similarly,

Let 120 distinct objects are divided into 24 groups of 5 objects in each group.

No. of ways of formation of groups

$= \frac{(120)!}{(5!)^{24} \cdot 24!} \in N$

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