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Eight chairs numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement
Eight chair 1 to 8
2 women choose the chair from 1 to 4 = ^{4}P_{2}
3 men choose the chair from remaining = ^{6}P_{3}
^{4}P_{2} x ^{6}P_{3}
If the letter of the word FATHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word FATHER is:
Rank of father
A five digit number divisible by 3 is to be formed using the number 0,1,2,3,4,5 without repetition The total number of ways this can be done is :
If the sum of digits of the number is divisible by 3 then number is divisible by 3
Total = 216
An office has 5 computers that are connected together in a linear network (i.e. they will be arranged in 5 position on one straight on one straight connecting cable, see figure below). Communication can go either way along the cable. In how many different ways they are arranged?
Total number of ways in which Six ‘+’ and four '' signs occur together is :
++++++
A bin of personal computer disks contains a large supply of disks from 4 different manufactures. In how many ways someone choose 6 disks from the bin?
a + b + c + d = 6
How many numbers greater than 1000, but not greater than 4000 can be formed with the digits 2,1,2,3,4 repetition of the digit being allowed?
Numbers greater than 1000 but less than 4000 formed with digit 0,1,2,3,4 will be
3.5.5.5+11 = 3751+1
= 375
20 persons were invited for a party. The number of ways in which they and the host can be seated at a circular table such that two particulars persons be seated on either side of the host is:
2(18!)
The number of triangle whose vertices are at the vertices of an octagon but none of whose sides come from the sides of the octagon is:
A man has 7 relatives, 4 of them are ladies and 3 gentlemen. His wife has 7 relatives, 3 of them are ladies and 4 gentleman. Then the number of ways the couple can invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man’s relative and 3 of the wife's relatives is equal to:
A box contain two white balls, three black balls and 4 red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw is:
2W, 3B, 4R
1st method
At least one black ball out of 3 ball
= 84  20 = 64
2nd method
If in a party everybody shake hand with everybody else and there are 36 handshakes in all how many persons are there in the party?
If ^{15}C_{3r} = ^{15}C_{3r+3'} then r =
There are 3 copies each of 4 different books in how many way can they be arranged in a shelf?
The sum of all the numbers that can be formed with the digits the 2,3,4,5 taken all at a time is :
The number of ways in which one or more balls can be selected out of 10, 9 green and 7 blue balls is:
Total ways (10 + 1) (9 + 1) (7 + 1)1
= 110 x 8  1
= 880 1 = 879
The number of ways in which a score of 11 can be obtained from a throw by three persons each throwing a single dice is :
It is equal to sum of three integral values being equal to 11 with each of them lying from 1 to 6 i.e. 3 + 4 + 5 + 6 + 5 + 4 = 27 ways
At an election, three ward of a town are canvassed by 4,5 and 8 men respectively, if 20 men are voluntier, in how many ways can they be allotted to the different wards?
How many different permutation can be formed from the letter of the word EXAMINATION taken four at a time?
A tea party is arranged for 16 people along table with eight chair on each side, four men wish to sit on one particular side and two on the other side. In how many ways they can be seated?
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