First slide

Permutations

Question

In a certain test, a_i students gave wrong answers to at least i questions where i = 1, 2, 3, …, k. No student gave more than k wrong answers. The total number of wrong answers given is

Moderate

A

a₁ + a₂ + … + a_k
B

a₁ + a₂ + … + a_{k – 1}
C

a₁ + a₂ + … + a_k+1
D

None of these

Solution

Total number of wrong answers
$\begin{array}{l} = 1 \cdot (a_{1} - a_{2}) + 2 \cdot (a_{2} - a_{3}) + \dots + (k - 1) (a_{k - 1} - a_{k}) + {ka}_{k} \\ = a_{1} + a_{2} + a_{3} + \dots + a_{k} \end{array}$

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