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#1 2008-11-21 22:34:25
- ganesh
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Pre-University Mathematics
1. If
find n.
2. If
find n.
3. From 6 boys and 4 girls, 5 are to be selected for admission to a particular course. In how many ways can this this be done if there must be exactly 2 girls?
4. Find the number of diagonals in a polygon of a side. How many triangles can be made?
5. Find the number of arrangements in which 6 boys and 4 girls can be arranged in a line so that all the girls sit together and all the boys sit together.
6. A family of 4 brothers and 3 sisters are to be arranged for a photograph in one row. In how many ways can they be seated if all the sisters sit together.
7. If 6 times the number of permutations of n things taken 3 together is equal to 7 times the number of permutations of (n-1) things choses 3 at a time, find n.
8. In an election, a voter may vote for any number of candidates not greater than the number to be chosen. There are 7 candidates and 4 members are chosen. In how many ways can a person vote?
9. Using Binomial theorem, find the value of
.
10. Find the coefficient of in the expansion of
.
Character is who you are when no one is looking.
#2 2009-05-22 09:32:35
- bobbym
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Re: Pre-University Mathematics
Hi ganesh;
These are pretty old so I won't hide them.
#1
n=8
#2 ignoring the trivial 0 and 1:
n=5
#9
By the binomial theorem:
If we say x=100 and y= -1 and we plug these into the RHS of the above identity. We get;
#10
Last edited by bobbym (2009-05-24 11:46:04)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2009-08-17 06:20:09
- rzaidan
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Re: Pre-University Mathematics
Hi ganesh
problem no. 7 :
6(nC3)=7((n-1)C3)
6*n(n-1)(n-2)/(3*2*1) = 7 (n-1)(n-2)(n-3)/(3*2*1) so by cancellation ((Hint : n ≥3))
6n = 7(n-3) or 6n = 7n - 21 so n=21
Best Regards
Riad Zaidan
#4 2009-08-17 06:24:24
- rzaidan
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Re: Pre-University Mathematics
Hi ganesh
problem no. 3 :
The no. of ways = (6C3)(4C2)= 6(5)(4)/3(2)(1) * 4(3)/2(1)
=20*6=120
Best Regards
Riad Zaidan
#5 2009-08-17 06:27:44
- rzaidan
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Re: Pre-University Mathematics
Hi ganesh
problem no. 4:
The no. of diagonals= a(a-3)/2
The no. of triangles= aC3=a(a-1)(a-2)/3*2*1
Best Regards
Riad Zaidan
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#6 2009-08-17 06:33:08
- rzaidan
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Re: Pre-University Mathematics
Hi ganesh
problem no. 5:
The number of arrangements= 2 * 6! * 4!
2*6(5)(4)(3)(2)(1)*4(3)(2)(1)
Notice that the 2 in the expression denotes the number of cases for the side can be chosen
( left or right of the line)
Best Regards
Riad Zaidan
#7 2009-08-17 06:39:06
- rzaidan
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Re: Pre-University Mathematics
Hi ganesh
problem no. 6:
First we choose the three neighbouring positions for the girls by 5 ways so
they can be seated by 5 * 4! * 3! =5(4)(3)(2)(1)*(3)(2)(1)=720 ways
Best Regards
Riad Zaidan
Online
#8 2009-08-17 07:15:25
- bobbym
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Re: Pre-University Mathematics
Hi ganesh;
Last edited by bobbym (2009-08-17 07:20:33)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.