Chapter 12.1, Problem 38STP

To determine

Find the number of sequences of hits and misses.

Answer to Problem 38STP

  $45$

Explanation of Solution

Given information:

Ofelia is taking ten shots in the intramural free-throw shooting competition. She makes $8$ shots and misses $2$ .

Calculation:

Here, there are $n$ different distinguishable objects out of which one object is repeated $r_1$ times, another is repeated $r_2$ times and so no.

  $\therefore \frac{n!}{r_1!\times r_2!\mathrm{.....}\times r_k!}$

Now, as there are $10hits$ and misses. Out of $10,8hitsand2miss$ .

Thus, the total number f possible sequences are:

  $\frac{10!}{8!2!}=45$

Hence, the required answer is $45$ .