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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

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