**Mrs. G.R. Valsala **

**Date of submission : 26/10/09**

**(Maths optional)**

**PERMUTATIONS AND COMBINATIONS**

- How many words, with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

- How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

- A committee of 7 has to be formed from nine boys and four girls. In how many ways can this be done when the committee consists of:

- Exactly 3 girls? (ii) At least 3 girls? (iii) Almost 3 girls?

**BINOMIAL THEOREM**

Using Binomial Theorem, evaluate each of the following:

4. (96)^{3 }

5. (102)^{5 }

6. (101)^{4 }

7. Using Binomial Theorem, indicate which number is larger (1.1)^{10000} or 1000.

8. Find (x+1)^{6} + (x-1)^{6}. Hence or otherwise evaluate (√2 + 1)^{6} + (√2 – 1)^{6}.

9. Show that 9 ^{n+1} – 8n – 9 is divisible by 64, whenever n is a positive integer.

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