A mother and father have seven children, and the family receives an invitation with four tickets to the circus. If the

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A mother and father have seven children, and the family receives an invitation with four tickets to the circus. If the family decides to randomly select the four members who get to attend the circus, but determine that the chosen group must include at least one of the mother and father, how many different groups are possible to send to the circus?

A. 70
B. 84
C. 91
D. 108
E. 126


OA C

Source: Veritas Prep

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BTGmoderatorDC wrote:
Mon Aug 23, 2021 7:01 pm
A mother and father have seven children, and the family receives an invitation with four tickets to the circus. If the family decides to randomly select the four members who get to attend the circus, but determine that the chosen group must include at least one of the mother and father, how many different groups are possible to send to the circus?

A. 70
B. 84
C. 91
D. 108
E. 126


OA C

Source: Veritas Prep
We have two ways to select

1) Mother or father along with \(3\) of their children.
\(2C1\ast 7C3=2 \times 35=70\)

2) Both mother and father along with \(2\) of their children.
\(2C2\ast 7C2= 1\times 21\)

So, \(70+21=91 \Longrightarrow\) C