A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at …

Question

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:

Accepted Answer

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

Solutions · 1