There are 10 contenders in a karate competition, 5 in division A and 5

Question

There are 10 contenders in a karate competition, 5 in division A and 5 in division B. How many possible ways are there for the contenders to place 1st and 2nd in both divisions?

A. 20
B. 25
C. 100
D. 200
E. 400

gmatophobia · Answer

bill96251  - The objective of the question is to place the contenders in two places (1st and 2nd) in both divisions. To do so, we need to first select two contenders from each division. Once we have done that, the two children can be arranged in the two places.

1) Select two children from Division A and Select two children from Division B

Each division has 5 children, so 2 children out of 5 can be selected by  ^5C_2  ways.

2) Arrange / Place the contenders in 1st and 2nd positions

Once, we have selected two children, the children can be placed in 2! ways.

For each class the number of ways we can select and arrange =  ^5C_2 * 2! = 20

As we are dealing with two classes, the number of ways the contenders to place 1st and 2nd in both divisions = 20 * 20 = 400

Hope this helps.

RenB · Answer

This is the approach I used- In counting questions when there are multiple events and we are required to find out the number of combinations, 'AND' implies MULTIPLICATION of the number of possibilities for each event 'OR' implies 'ADDITION' of the number of possibilities for each event In this question, I understand that we are required to find the total number of possibilities for- (Event A)- 1st and 2nd position in Division A AND (Event B)- 1st and 2nd position in Division B Thus required: Number of possibilities for Event A * Number of possibilities for Event B For Event A: 1st position: Any 1 of the 5 students can be 1st. Thus 5C1 ways= 5 AND 2nd Position: 1 student is 1st. Thus 4 remain. Number of ways one of the remaining 4 students will be second= 4C1=4 Total ways for Event A= 5*4= 20 Similarly number of ways for event B= 20 Thus total number of ways for both divisions= Event A and Event B= 20*20= 400

if this helped you

Also thanks, helped me revise the concept!

Kinshook · Answer

Given: There are 10 contenders in a karate competition, 5 in division A and 5 in division B. 
Asked: How many possible ways are there for the contenders to place 1st and 2nd in both divisions?

Number of possible ways to place the contenders to place 1st and 2nd in both divisions = (5*4) * (5*4) = 400

IMO E

Archit3110 · Answer

ways to the contenders can be 1st or 2nd in two divisions of 5 each
(5*4 ) * ( 5*4)
5*4 refers to A and other to B

OPTION E

bumpbot · Answer

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There are 10 contenders in a karate competition, 5 in division A and 5

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