JEE MAIN - Mathematics (2021 - 24th February Morning Shift - No. 7)
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 :
1050
575
560
1625
Explanation
Given,
Number of Indians = 6
Number of foreigners = 8
Committee of at least 2 Indians and double number of foreigners is to be formed. Hence, the required cases are
(2I, 4F) + (3I, 6F) + (4I, 8F)
= $${}^6{C_2} \times {}^8{C_4} + {}^6{C_3} \times {}^8{C_6} + {}^6{C_4} \times {}^8{C_8}$$
= (15 $$\times$$ 70) + (20 $$\times$$ 28) + (15 $$\times$$ 1)
= 1050 + 560 + 15 = 1625
Number of Indians = 6
Number of foreigners = 8
Committee of at least 2 Indians and double number of foreigners is to be formed. Hence, the required cases are
(2I, 4F) + (3I, 6F) + (4I, 8F)
= $${}^6{C_2} \times {}^8{C_4} + {}^6{C_3} \times {}^8{C_6} + {}^6{C_4} \times {}^8{C_8}$$
= (15 $$\times$$ 70) + (20 $$\times$$ 28) + (15 $$\times$$ 1)
= 1050 + 560 + 15 = 1625
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