IIT JEE , AIEEE Forum - Mathematics , Algebra

umang

In how many ways can a cricketer make a century with fours and sixes ????

frenied

i think it should be the number of solutions of 4x+6y=100.now use co-efficient method to find no of solutions to this eqn.i dont know the method otherwise i would've done it.

umang

yes , I also think this is the only way !!!!!

aneeshrox

It can be done using this equation (4x+6y=100) also
=>4x=10-6y
you just have to find those probable values of y which would give integral values of x
on solving 8 set of solution are possible
(25,0);(22,2);(19,4);(16,6);(13,8);(10,10);(7,12);(4,14)
was this only the required answer or do you also want the to be permuted

abhijeet_0201

refer to post
http://www.goiit.com/posts/list/5466.htm
the ques is solved there.
thank u

phyana

The total no. of ways =8.

By permuting the possiability we get

(24 C 2 )+ (23 C 4) +( 22 C 6 )+ (21 C 8 )+ (20 C 10 )+ (19 C 12) +(18 C 14) +(17 C 16)

aneeshrox

you are wrong
the correct method is
possible ways
(25,0);(22,2);(19,4);(16,6);(13,8);(10,10);(7,12);(4,14);(1,16)
now we have to permute each case to get the result
(25!)/(25!)+(24)!/(22!2!)+(23!)/(19!4!)+(22!)/(16!6!)+(21!)/(13!8!)+(20!)/(10!)(10!)+(19!)/(7!12)!+(18!)/(14!4!)+(17!)/(16!)
calculate this and you will get the result
thank you.........

ankurgupta91

hey aneesh u r quite rght
bt u hv forgot to mention the case of( 1 four and 16 sixes)
so the total cases
(25,0);(22,2);(19,4);(16,6);(13,8);(10,10);(7,12);(4,14);(1,16)
nd for the result
(25!)/(25!)+(24)!/(22!2!)+(23!)/(19!4!)+(22!)/(16!6!)+(21!)/(13!8!)+(20!)/(10!)(10!)+(19!)/(7!12)!+(18!)/(14!4!)+(17!)/(1!16!)
thats the right answer
thanks........

Asmita

kghedriu

.............What is the............ DIPHONTINE EQUATION??

pls explain.....................................

Asmita

Diphontine eq. r eq. in 2 variables having integral sol. since 4 getting a unique sol. we need 2 such eq. so there r many possible sol. 4 diphontine eq.

harsh_desai_25

now for here we assume sixes to be x and fours to be y
hence a cricketer can score a century with 14x+4y=100
now on substituing the value of x and y we get 100
do rate me

frenied

hey asmita cud u please explain ur method??i have tried to solve this by an alternate method.experts do look at it to see if its correct.
4x=100-6y
x=25-(6y/4)
now x we know has to be integral.so 6y/4 should be integral and less than 100 ie 6y should be a multiple of 4 (since integer-integer only can give an integer).6y is already a multiple of 6 and nowby above argument it shud also be a multiple of 4.so in short 6y should be a multiple of lcm of 4 and 6 that is 12.and no.of multiples of 12 which are less than 100 (refer to equation 4x=100-6y where 6y is a multiple of 12) is 9 including 0 and 96.so ur answer is correct=9.

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