drraju's problem please solve it

[munimM]

1.Given that there are 10 balls and 10 bags and 3 balls are of same kind. In how many ways these ‘10’ balls can be arranged in 10 bags, such that no bag should be left empty?
(Similar to this)

2.In a hotel, the room numbers of a floor are numbered from 101 to 550. If particular rooms selected are of numbers that start with 1, 2, 3 and lasts with 4, 5, 6 then in how many ways the rooms can be selected?
(Similar to this)

3.A crew of 12 members has to be seated around a dinning table. If the distance between each person to the other is 2.5ft, then what is the minimum length of the dinning table?

4. In an apartment 92% have cars and 14% have bikes and everyone in the apartment have either bike or a car.
Col A: Fraction of the people having car as well as bike
Col B: 1/10

[tushar4036]

1. 10!/3!

4. 92-x+14-x+x=100
x=6

compare 6/100 & 1/10
col B IS GREATER

[ace_gre]

2. All room numbers are three digits.
Hundred's digit is 1,2,3 so 3 ways of choosing first digit.
Ten's digit can be 0-9 so 10 ways of choosing second digit.
Unit's digit can be 4,5,6 so 3 ways of choosing it.

total # of ways = 3 X 10 X 3 = 90 ways.

3. Square table will have the smallest length. Each side seats 4 people so 3 spaces in-between= 3 X 2.5=7.5 ft.

Thanks!

[Curly213]

to ace gre .. if u a squar table and each side 4 people then we should have 16 people .. if iam gettin it right... got the same for 2 and 4 .. but for number 1 ...could s.o. explain it to me why should we divide it by 3! ..iam not gettin the point... because we want to know in how many ways so for the firstr 10 ways for the 2nd 9.....and so on=)

[ace_gre]

Curly213,

Here is the seating arrangement I am looking at (not lining up properly. Going clockwise, 1234 horizontal top, below 4 is 5,6,7 and so on..)

1 2 3 4

12 5

11 6

10 9 8 7

In this case minimum length would be 7.5 ft.

Thanks!