First slide

Combinations

Question

$A s c i e n t i f i c c o m m i t t e e i s t o b e f o r m e d f r o m 6 I n d i a n s a n d 8 f o r e i g n e r s, w h i c h i n c l u d e s a t l e a s t 2 I n d i a n s a n d$ $d o u b l e t h e n u m b e r o f f o r e i g n e r s a s I n d i a n s . T h e n t h e n u m b e r o f w a y s, t h e c o m m i t t e e c a n b e f o r m e d i s$

Moderate

A

1625
B

560
C

1050
D

$575$

Solution

$\begin{array}{l} (2 I, 4 F) + (3 I, 6 F) + (4 I, 8 F) =^{6} {C_{2}}^{8} C_{4} +^{6} {C_{3}}^{8} C_{6} +^{6} {C_{4}}^{8} C_{8} \\ = 15 \times 70 + 20 \times 28 + 15 \times 1 \\ = 1050 + 560 + 15 \\ = 1625 \end{array}$

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