Question

A boy has to climb 10 steps. He tosses one coin. If head appears, he climbs a single step. If tail appears, he climbs 2 steps. In how many ways can he climb 10 steps?

• A. 90
• B. 88
• C. 92
• D. 89

Answer 1

The correct option is D

89

$\begin{array}{ccc}SingleStep& DoubleStep& Numberofways\\ 10& 0& 1\\ 8& 1& \frac{9!}{8!}=9\\ 6& 2& \frac{8!}{6!\times 2!}=28\\ 4& 3& \frac{7!}{4!\times 3!}=35\\ 2& 4& \frac{6!}{2!\times 4!}=15\\ 0& 5& 1\end{array}$

Total number of ways = 1 + 9 + 28 + 35 + 15 + 1 = 89. Option(d)