Question

Match the statements/ Expressions in Column I with Column II :

Answer 1

$ENDEANOEL$

$ENDEA:$

Number of ways $=5$

Total number of permutation $=5!$ Ways

$A⟶1$

$E$ fixed in first and last places

Therefore number of ways

$=\frac{7!}{2!}=2!\times 5!B⟶4$

$D,L,N$ are not in last $5$ positions

Therefore number of permutations

$=\frac{4!}{2!}\times \frac{5!}{3!}=2\times 5!$

In which they occur

$=9\times 5!=2\times 5!=7\times 5!$

$C⟶3$

The number of permutations in which the letter $A,E,O$ occur in odd positions only.

Total numbers of odd positions $=5$

Permutation of $AEEEO$ are $\frac{5!}{3!}$

Total numbers of even positions $=4$

Permutation $=\frac{4!}{2!}$

Total permutations$\frac{4!}{2!}\times \frac{5!}{3!}=2\times 5!$

$D⟶2$