made easy 2019

Question

In how many ways can we choose a cricket team of 11 players out of 10 batsman,5 bowlers,2 keepers such that the team has atleast 4 bowlers?

i am getting 4884;

my approach

$\binom{5}{4}* \binom{10}{7}*\binom{2}{0}$ + $\binom{5}{4}* \binom{10}{6}*\binom{2}{1}$ + $\binom{5}{4}* \binom{10}{5}*\binom{2}{2}$+$\binom{5}{5}* \binom{10}{6}*\binom{2}{0}$ +$\binom{5}{5}* \binom{10}{5}*\binom{2}{1}$ + $\binom{5}{5}* \binom{10}{4}*\binom{2}{2}$

Comments

$4$ bowlers  + $5$ bowlers

$={}^5C_4*{}^{12}C_7+{}^5C_5*{}^{12}C_6$

or simply = $={}^5C_4*{}^{13}C_7$

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cant we have  further choice on number of batsman & keepers???

@Shobhit Joshi

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${}^{12}C_6$ covers all the choices you can create when the number of bowlers are 4 and same when 5

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then why the anwer coming is not same?

any idea?

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okay, answer is same in both the cases;

okay!!! answer was given wrong in the key!!

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this is what they have done, wrong calculation

don't even have 4884 as option; they haven't marked none of these as option ;

 

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mistake happens