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6.Permutation and Combination
medium
A scientific committee is to be formed from $6$ Indians and $8$ foreigners, which includes at least $2$ Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is
A
$1625$
B
$575$
C
$560$
D
$1050$
(JEE MAIN-2021)
Solution
| Indians | Foreigners | Number of ways |
| $2$ | $4$ | ${ }^{6} C _{2} \times{ }^{8} C _{4}=1050$ |
| $3$ | $6$ | ${ }^{6} C _{3} \times{ }^{8} C _{6}=560$ |
| $4$ | $8$ | ${ }^{6} C _{4} \times{ }^{8} C _{8}=15$ |
Total number of ways $=1625$
Standard 11
Mathematics
