How many words starting with letter D can be formed by taking all letters from word DELHI, so that the letters are notrepeated?
Explanation
Concept:
If there are m ways for happening of an event A, and corresponding to each possibility there are n ways for happening of event B, then the total number of different possibilities for happening of events A and B are:
- Either event A OR event B alone = m + n.
- Both event A AND event B together = m × n.
- A number is divisible by 2 if its units digit is either 0, 2, 4, 6 or 8.
Permutations/Arrangements:
- The number of ways in which r objects can be arranged in n places is nPr=(n−r)!n!.
- The number of ways in which n objects can be arranged in n places is nPn=n!.
- n! = 1 × 2 × 3 × ... × n.
- 0! = 1.
Calculations:
The number of letters in the word DELHI = 5.
Since, D has to be the first letter, the number of ways in which the first letter can be written is 1.
The remaining 4 letters can be written in any order/arrangement of the remaining 4 letters (ELHI).
∴ The number of ways of writing the 4 letters = 4! = 4 × 3 × 2 × 1 = 24.
∴ The total number of ways of writing the 5 letters = 1 × 24 = 24.
