Question

The total number of three-letter words that can be formed from the letter of the word SAHARANPUR is equal to

• A. $210$
• B. $237$
• C. $247$
• D. $227$

Answer 1

The correct option is C $247$

Case 1: No repetition: ${}^7{P}_3=210$
Case2: One letter appears twice: The repeating letter may be selected from A or R in ${}^2{C}_1=2$ ways. The remaining letter may be selected from the remaining 6 possibilities in $6$ ways. Now, arrangement needs to be done. Thus, total number of ways = ${}^2{C}_1\times 6\times \frac{3!}{2!}=36$ ways.
Case 3: One letter appears thrice: The only possibility is $AAA$ i.e. $1$ way.
Thus, answer $=210+36+1=247$.
Hence, (c) is correct.