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6.Permutation and Combination
easy
$22$ ખેલાડીઓ પૈકી $10$ ખેલાડીઓની એક ટીમ કેટલી રીતે બનાવી શકાય. જેમાં $6$ ચોક્કસ ખેલાડીનો હંમેશા સમાવેશ થાય અને $4$ ચોક્કસ ખેલાડીનો હંમેશા નિકાલ થાય ?
A
$^{22}C_{10}$
B
$^{18}C_3$
C
$^{12}C_4$
D
$^{18}C_4$
Solution
${ }^{12} C_4$
First from $22$ players, we take out $4$ particular players, who are excluded always.
Now, total numbers of players in consideration are $22-4=18$.
We need to select $10$ players out of these $18$ players. As it is given that $6$ particular players are always included, we don't have any flexibility over these $6$ players. So, number of players available for selection $=18-6=12$. Out of $10$ vacancies, $6$ are already filled and $4$ vacancies are left.
So, from $12$ players,$4$ players can be selected in ${ }^{12} C _4$ ways.
Standard 11
Mathematics
