“Everything you’ve ever wanted is on the other side of fear.” — George Addair

# Lecture - 3 Chapter 7 Permutations and Combinations

Number of Permutations when an alphabet repeat

**Example 14. **Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that **(i)** all vowels occur together **(ii)** all vowels do not occur together.

**Example 16. **Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, **(i)** do the words start with P **(ii)** do all the vowels always occur together **(iii)** do the vowels never occur together**(iv)** do the words begin with I and end in P?

NCERT Exercise 7.3 |

**Question 10. **In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

**Question 11. **In how many ways can the letters of the word PERMUTATIONS be arranged if the **(i)** words start with P and end with S, **(ii)** vowels are all together, **(iii)** there are always 4 letters between P and S?