2^10 * 4^10 * 6^10*8^10 = 2^70 * 3^10
2^2 * 3^2 = 36
So, the right most digit = 6
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NA
SHSTTON
7
Solv. Corr.
4
Solv. In. Corr.
11
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There is a 7-digit telephone number with all different digits. If the digit at extreme right and extreme left are 5 and 6 respectively, find how many such telephone numbers are possible?
If the digit at extreme right and extreme left are 5 and 6 respectively.
So, the 7 digit number is : 6 _ _ _ _ _ 5
Since repetition of digits are not allowed the second digit can be chosen from (0,1,2,3,4,7,8,9) 8 of the remaining digits.
5 spaces are left, hence 8P5=6720
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NA
SHSTTON
3
Solv. Corr.
3
Solv. In. Corr.
6
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In how may ways can 'mn' things be distributed equally among n groups
mn into n groups
= (mn)! / (m! m! ....n times * n!(n groups are similar))
= (mn)! / (m!)^n * n!
Workspace
NA
SHSTTON
17
Solv. Corr.
9
Solv. In. Corr.
26
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There are 20 persons sitting in a circle. In that there are 18 men and 2 sisters. How many arrangements are possible in which the two sisters are always separated by a man?
Let the first sister name is A. Now she can sit any where in the 20 places (Symmetrical). Now her sister B can sit to her left or right in 2 ways. Now the remaining 18 persons can be sit in 18 places in 18! ways. Total = 18! * 2
Workspace
NA
SHSTTON
10
Solv. Corr.
9
Solv. In. Corr.
19
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In how many ways a team of 11 must be selected a team 5 men and 11 women such that the team must comprise of not more than 3 men.
5 men and 11 women and not more than 3 men
1st way= 1men and 10 women= 5C1 * 11C10
2nd way= 2 men and 9 women=5C2 *11C9
3rd way= 3 men and 8 women= 5C3* 11C8
4th way= 0 men and 11 women=5C0* 11C11
Adding all we get= 2256.
Workspace
NA
SHSTTON
3
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8
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11
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There are ten points marked on a straight line, and another 11 points marked on a line parallel to this one. How many triangles could be formed using these points ?
A manufacturer of chocolates makes 6 different flavors of chocolates. The chocolates are sold in boxes of 10.
How many "different" boxes of chocolates can be made?
If n similar articles are to be distributed to r persons, x1+x2+x3......xr=n each person is eligible to take any number of articles then the total ways are n+r?1Cr?1
In this case x1+x2+x3......x6=10
In such a case the formula for non negative integral solutions is n+r?1Cr?1 Here n = 6 and r = 10. So total ways are 10+6?1C6?1 = 3003
Workspace
NA
SHSTTON
3
Solv. Corr.
5
Solv. In. Corr.
8
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Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.
Division of m+n+p objects into three groups is given by (m+n+p)!m!*n!*p! But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!*3!*3!*12! + (7)!1!*2!*4! + (7)!1!*1!*5!*12! = 70 + 105 + 21 = 196
Workspace
NA
SHSTTON
10
Solv. Corr.
5
Solv. In. Corr.
15
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The crew of a rowing team of 8 members is to be chosen from 12 men (M1, M2,...., M12) and 8 women (W1, W2,..., W8), such that there are two rows, each row occupying one the two sides of the boat and that each side must have 4 members including at least one women. Further it is also known W1 and M7 must be selected for one of its sides while M2, M3 and M10 must be selected for other side. What is the number of ways in which rowing team can be arranged.
We need two person for one side and 1 women for the another side. We select that women in 7 ways. Now that second side people can sit in 7*4! ways.
Now for the first side we need two people from the remaining 14. So this can be done in 14C2 ways and this side people can sit in 4C2*4! ways.
Again the first group may take any of the two sides. So total ways are 2*7*4!*14C2*4!
Workspace
NA
SHSTTON
6
Solv. Corr.
6
Solv. In. Corr.
12
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Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if mr smith never stand next to mrs smith then how many way group arrange in row.
Mr and Mrs smith never be together so out of 20 (with both them) 19 can b any place so total = 19!
20 because their invitees are with their spouses.
Also 1 of them can stand with other so 18 places
So total is 18*19!
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