Jee Main 2024 31 01 2024 Shift1 - Question5

Answer: (3)

Solution:

4-letter words formed by

DISTRIBUTION

$D \rightarrow 1$

I $\rightarrow 3$

$S \rightarrow 1$

$T \rightarrow 2$

$R \rightarrow 1$

$B \rightarrow 1$

$U \rightarrow 1$

$O \rightarrow 1$

$N \rightarrow 1$

(i) 4 alike $=0$

(ii) 3 alike +1 diff $={ }^{1} C _1 \times{ }^{8} C _1 \times \frac{4 !}{1 !}$

(iii) $2 A B C$ type

$\Rightarrow{ }^{2} C _1 \cdot{ }^{8} C _2 \cdot \frac{4 !}{2 !}$

(iv) $2 A 2 B={ }^{2} C _2 \cdot{ }^{4} C _2$

(v) $A B C D$ type : ${ }^{9} C _4 \times 4$!

$\Rightarrow$ Total $=3734$