15 C3 + 15 C5 + .... + 15 C15 will be equal to: - Vidyadip

MCQ

¹⁵C₃ + ¹⁵C₅ + .... + ¹⁵C₁₅ will be equal to:

A
2¹⁴
B
2¹⁴ - 15
C
2¹⁴+ 15
D
2¹⁴ − 1

✓

Answer

2¹⁴ - 15

Solution

We know

¹⁵C₁ + ¹⁵C₃ + ¹⁵C₅ + .....¹⁵C₁₅ = 2^{15 - 1}

$\therefore$ ¹⁵C3 + ¹⁵C₅+ ... + ¹⁵C₁₅ = 2¹⁴ - 15

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