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There are 6 players in a cricket which is to be sent to Australian tour. The total number of members is 12.
Q. If 2 particular member is always included
- a)210
- b)270
- c)310
- d)420
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There are 6 players in a cricket which is to be sent to Australian tou...
Answer – a) 210 Explanation : only 4 players to select, so it can be done in 10c4 = 210
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There are 6 players in a cricket which is to be sent to Australian tou...
Given:
- 12 members in total
- 6 players to be sent to Australian tour
- 2 particular members always included
To find:
- Total number of possible ways to select 6 players from 12 members with the 2 particular members always included
Solution:
1. The 2 particular members are always included, so we only need to select 4 more players from the remaining 10 members.
2. The number of ways to select 4 players from 10 members can be calculated using combinations formula:
nCr = n! / r!(n-r)!
where n = 10 and r = 4
nCr = 10! / 4!(10-4)!
= (10*9*8*7*6*5*4*3*2*1) / [(4*3*2*1)*(6*5*4*3*2*1)]
= 210
3. Therefore, the total number of possible ways to select 6 players from 12 members with the 2 particular members always included is 210.
Answer: Option A) 210.
- 12 members in total
- 6 players to be sent to Australian tour
- 2 particular members always included
To find:
- Total number of possible ways to select 6 players from 12 members with the 2 particular members always included
Solution:
1. The 2 particular members are always included, so we only need to select 4 more players from the remaining 10 members.
2. The number of ways to select 4 players from 10 members can be calculated using combinations formula:
nCr = n! / r!(n-r)!
where n = 10 and r = 4
nCr = 10! / 4!(10-4)!
= (10*9*8*7*6*5*4*3*2*1) / [(4*3*2*1)*(6*5*4*3*2*1)]
= 210
3. Therefore, the total number of possible ways to select 6 players from 12 members with the 2 particular members always included is 210.
Answer: Option A) 210.
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There are 6 players in a cricket which is to be sent to Australian tou...
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