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Question
The value of (5C0 + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5) is:
Options
26 – 2
25 – 1
28
27
Solution
26 – 2
Explanation:
(5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5) + (5C1 + 5C2 + 5C3 + 5C4)
= 25 + (5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5) – (5C0 + 5C5)
= 25 + 25 – (1 + 1) (∵ Adding and subtracting of 5C0 and 5C5)
= 2(25) – 2 (∵ 5C0 = 5C5 = 1)
= 26 – 2
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