Question

There are 10 multiple choice questions on a test , with 5 possible answers to each question. What is probability of getting 6 out of 10 correct ?

Answer 1

Total number of ways of answering the 10 questions is 5¹⁰

Number of ways of answering 6 out of 10 questions correct is ${10\choose 6}\cdot4^4$ = $210\times 256$

Probability of getting 6 out of 10 correct questions is $\frac{210\times256}{5^{10}} = \frac{10752}{5^{9}} = 0.0055$