General Questions
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Numbers between 100 and 1000 = 900
Unit digit could take any value of the 9 values (0 to 9, except 6)
Tens Digit could take any value of the 9 values (0 to 9, except 6)
Hundreds digit could take any value of the 8 values (1 to 9, except 6)
Numbers between 100 and 1000 which do not have digit 6 in any place = 9 × 8 × 8 = 648
Numbers between 100 and 1000 which have at least one digit as 6
= (900 - 648) = 252
Circular Permutation
'n' objects can be arranged around a circle in (n1)!
If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.
| i.e., number of arrangements = | (n - 1)! |
| 2 |
You can choose the 7 people to sit in the first table in 15C7 ways.
After selecting 7 people for the table that can seat 7 people, they can be seated in: (71)! = 6!
The remaining 8 people can be made to sit around the second circular table in: (81)! =7! Ways.
Hence, total number of ways: 15C8 × 6! × 7!
The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is :
(3 x 3 x 3 x 3 x 3) = 35 = 243
The word EDUCATION is a 9 letter word, with none of the letters repeating.
The vowels occupy 3rd, 5th, 7th and 8th position in the word and the remaining 5 positions are occupied by consonants
As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the aforementioned 4 places and the consonants can occupy 1st, 2nd, 4th, 6th and 9th positions.
The 4 vowels can be arranged in the 3rd, 5th, 7th and 8th position in 4! Ways.
Similarly, the 5 consonants can be arranged in 1st, 2nd, 4th, 6th and 9th position in 5! Ways.
Hence, the total number of ways = 4! * 5!.