111 match one ball? or can the ball be changed?
find the no of ways...in which 18 identical balls can be used in 15 different cricket matches
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12 Answers
11The answer is 15C18 = 18*16*17/3*2*1 = 6*8*17 = 48*7
=336 ways
62I am not able to understand the answer!!
The answer should be 1 ... if in each match only one ball can be used!
11wat is going on
THE CONCEPT :NUMBER OF WAYS OF ARRANGING n IDENTICAL OBJECTS TO r GROUPS IS
n+r-1Cn IF EMPTY GROUP IS ALLOWED
AND
n-1Cr-1 WHEN EMPTY GROUP IS NOT ALLOWED
SO THE ANSWER IS OBVIOUSLY
17C14 (AS A BALL IS ESSENTIAL 4 A MATCH [3][3][3])
11YUP THIS WAS DONE IN OUR CLASS
SO
THE QUESTION MUST BE
IN HOW MANY WAYS n IDENTICAL OBJECTS BE DISTRIBUTED IN r DIFFERENT GROUPS SUCH THAT EACH GROUP MAY HAVE ANY NUMBER OF OBJECT ???
the answer follows in the next post to avoid confusion!!!!!!!!!
11a1+a2+a3+a4..................+ar=n
0≤ai≤n and 1≤i≤r
now we have to find the coefficient of xn in the expansion of (x0+x1+x2+x3+x4..........+xn)r
or coefficient of xn in (1-xn+1/1-x)r (using G.P)
=coefficient of xn in (1-xn+1)r(1-x)-r
there is no coefficient of xn in 1-xn+1
so coefficient in (1-x)-rcould be evaluated as
r+n-1Cn
this is a very important technique both 4 IIT and AIEEEE
as questions r asked on it probably every year !!!!!!!!!!!
11@manipal your method is the case when more than one ball is allowed in a match.
But the question is the case when each match uses only one ball