Verified Solution • 2025–26 Session moderate

QJEEM21Ma4f70: JEE Main 2021 Mathematics - Class 11 JEEM21Ma4f70 Solution: A scientific committee is to be formed from 6 Indians and 8…

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 :

Multiple Choice Options

  • A 1050
  • B 575
  • C 560
  • D 1625

Step-by-Step Verified Solution

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)

= 6C2×8C4+6C3×8C6+6C4×8C8{}^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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