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.
