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A jousting tournament requires that a team consist of two knights and two squires...

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A jousting tournament requires that a team consist of two knights and two squires...

by swerve » Fri Mar 20, 2020 5:16 pm

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A jousting tournament requires that a team consists of two knights and two squires. The Merry Band is forming a team from five knights and three squires. How many different lineups can The Merry Band field?

A. 10
B. 13
C. 15
D. 30
E. 120

The OA is D

Source: Magoosh
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Re: A jousting tournament requires that a team consist of two knights and two squires...

by deloitte247 » Sat Mar 21, 2020 7:30 am
- 1 team consists of 2 knights and 2 squires
- The Merry band has 5 knight and 3 squires
- How many different team line ups can the Merry Band field?
Choosing 2 knights out of 5 knights
$$=5C_2=>\frac{5!}{2!\left(5-2\right)!}$$
$$=\frac{5\cdot4\cdot3!}{2\cdot1\cdot3!}=\frac{20}{2}=10$$

Choosing 2 squires out of 3 squires
$$=3C_2=>\frac{3!}{2!\left(3-2\right)!}$$
$$=\frac{3\cdot2\cdot1!}{2\cdot1\cdot1!}=3$$

The total no. of different team lines = possible ways of choosing knights * possible ways of choosing squires = 10 * 3
= 30

Answer = D
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Re: A jousting tournament requires that a team consist of two knights and two squires...

by Scott@TargetTestPrep » Thu Mar 26, 2020 1:37 pm
swerve wrote: ↑
Fri Mar 20, 2020 5:16 pm
 A jousting tournament requires that a team consists of two knights and two squires. The Merry Band is forming a team from five knights and three squires. How many different lineups can The Merry Band field?

A. 10
B. 13
C. 15
D. 30
E. 120

The OA is D

Source: Magoosh
5C2 x 3C2 = [(5 x 4) / 2] x 3 = 10 x 3 = 30

Answer: D

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