Question

The number of words that can be formed with the letters of the word $PARALLEL$ so that all $L$ do not come together but both $A$ come together is

• A. $420$
• B. $3000$
• C. $720$
• D. None of these

Answer 1

Answer: (C)

$720$

When both A's are together, taking them as a single identity. number of ways $=\frac{7!}{3!}$ (as there are 3 L's)

When both A's and all 3 L's are together, taking them as two separate identity, number of ways $=5!$

Thus required number of ways $=\frac{7!}{3!}-5!=720$