Answer:
There are 220 ways by which the medals can be awarded to three of the 15 gymnast, if exactly one of the Americans wins a medal
Step-by-step explanation:
From the question, we have;
The number of gymnast in the Olympic women's competition = 15
The number of the gymnast who are Americans = 4
The number of medals awarded = 3 medals
The number of ways hat the medals can be awarded to the three of the gymnast if exactly one of the Americans wins a medal is given as follows;
The number of ways one of the medals can be won by one of the four Americans = ₄C₁ = 4 ways
The number of ways the other two medals can be won by the remaining 11 gymnast = ₁₁C₂ = 55 ways
Therefore, the total number of ways, 'N', the medals can be awarded to three of the 15 gymnast, if exactly one of the Americans wins a medal is given as follows;
N = ₄C₁ × ₁₁C₂
∴ N = 4 × 55 = 220
