1.How many ways 3-digit odd number can be formed by using the digit 1 to 9 when repetition is not allowed.?
Choose the first digit any of 9 ways.
Choose the second digit any of the 8 remaining ways.
Choose the third digit any of the 7 remaining ways.
Answer = 9·8·7 = 504
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2.how many numbers are there between 200 to 300 in which all of the digits are distint.?
Choose the fisrt digit as 2, that's 1 way.
Choose the second digit any of the 8 remaining ways.
Choose the third digit any of the 7 remaining ways.
Answer 1·8·7 = 56
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3.find the number of ways in which 5 boys and 4 girls can be seated
in a row so that no two girls are together.?
There are 15 ways they can be arranged
1. BBGBGBGBG
2. BGBBGBGBG
3. BGBGBBGBG
4. BGBGBGBBG
5. BGBGBGBGB
6. GBBBGBGBG
7. GBBGBBGBG
8. GBBGBGBBG
9. GBBGBGBGB
10. GBGBBBGBG
11. GBGBBGBBG
12. GBGBBGBGB
13. GBGBGBBBG
14. GBGBGBBGB
15. GBGBGBGBB
For each of those 15 ways there are 5! ways to seat the boys,
and 4! ways to seat the girls.
Number of ways = 15·5!·4! = 15·120·24 = 43,200 ways.
Edwin
