Question

Answer the following question using the appropriate counting​ technique, which may be either arrangement with​ repetition, permutations, or combinations. Be sure to explain why this counting technique applies to the problem.

How many possible birth orders with respect to gender are possible in a family with five ​children? (For​ example, BBBGG and BGBGGBBBGG and BGBGG are different​ orders.)

A. Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.
B. Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated.
C. Combinations because the selections come from a single group of items, no item can be selected more than once, and the order of the arrangement does not matter.
D. Arrangements with repetitions because the selections come from a single group of items, and the order of the arrangement matters.

Answer 1

Answer: A. Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.

Explanation:

• When the order of arranging things matters , we use permutations.
• When the order of arranging things does not matter , we use combinations.

To find the number of possible birth orders with respect to gender are possible in a family with five ​children we use Permutations because order of birth matter here.

Therefore , the correct answer is A. Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.