Respuesta :
Answer:
Tina can select and answer the essay questions on her test in 35 ways.
Step-by-step explanation:
The order in which she chooses the questions is not important. For example, choosing questions 1, 3 and 7 is the same as choosing 7, 3 and 1. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Three questions from a set of 7. So
[tex]C_{7,3} = \frac{7!}{3!(7-4)!} = 35[/tex]
Tina can select and answer the essay questions on her test in 35 ways.
Tina can select and answer the essay question on her test in 35 ways.
Number of ways to select 'r' objects out of 'n' objects is given by the expression,
Number of ways = [tex]^nC_r[/tex]
Since, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
If n = 7 and r = 3,
Number of ways to select 3 essays out of 7 will be,
Number of ways = [tex]^7C_3[/tex]
[tex]=\frac{7!}{3!(7-3)!}[/tex]
[tex]=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}[/tex]
[tex]=35[/tex]
Therefore, Tina can select and answer the essay question on her test in 35 ways.
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