Chapter 0.4, Problem 4E

To determine

To find: the number of different possible gloves are chosen from the different options.

Answer to Problem 4E

The number of possible combinations can be $48$ .

Explanation of Solution

Given:

Baseball glove manufacture makes a glove with $4$ sizes, $3$ position types, $2$ materials types and $2$ quality levels.

Concept used:

The number of ways of arranging $n$ different item in order is $n_1\times n_2\times n_3\times \mathrm{....}{n}_n$ .

The probability formula is used to compute the probability of an event to occur as:

  $P\left(A\right)=\frac{\text{Number of favorable outcome}}{\text{Total Number of favorable outcomes}}$ .

Calculation:

Consider a baseball glove manufacture makes a glove with $4$ sizes, $3$ position types, $2$ materials types and $2$ quality levels.

The number of possible combinations of gloves by the use of fundamental counting principle as follows:

Number of different combinations $=4\text{ sizes}\times 3\text{ positio types}\times 2\text{ material}\times 2\text{ quality levels}$ .

Simplifying it as follows:

Number of different combinations $=4\times 3\times 2\times 2=48.$

Hence, the number of possible combinations can be $48$ .