There are 16 teams divided in 4 groups. Every team from each group will play with each other once. The top 2 teams will go to the next round and so on the top two teams will play the final match. Minimum how many matches will be played in that tournament?
: In each group, total matches played = 4C2 = 6.
So total matches played in the first round = 6 * 4 = 24
Now top two teams from each group progress to the next round.
Now these 8 teams are pooled into 2 groups of 4 teams
. Total matches played in the second round = 6 * 2 = 12. (4C2=6 in each grp)
Now 4 teams progress to the next round.
Total matches played in the third round = 4C2 =6
From this round, 2 teams progress to the next round. And final will be played between them.
Total matches = 24 + 12 + 6 + 1 = 43
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4
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11
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Oranges can be packed in sets of 10 oranges in box type A or 25 oranges in box type B. A carton comprising of 1000 oranges of type a and b is packed. How many different combinations are possible in the number of type A and type B boxes while organizing the oranges?
The expression will be 10x+25y=1000
the above exp will be satisfied only with multiples of 2 up to 38.
so no. of combinations are 19.
if oranges are packed in type A boxes only= 1 way
if oranges are packed in type B boxes only= 1 way
so total = 19+1+1=21
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18
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40
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A number plate can be formed with two alphabets followed by two digits, with no repetition. Then how many possible combinations can we get?
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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21
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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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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!
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21
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14
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35
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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
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31
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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.
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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
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