bySayantani Barman Experta en el extranjero
Question: There are 7 red and 5 blue marbles in a jar. In how many ways 8 marbles can be selected from the jar so that atleast one red marble and atleast one blue marble remain in the jar?
- 460
- 490
- 493
- 455
- 445
Answer:
Solution with Explanation :
Approach Solution (1):
Total ways to select 8 marbles out of 7 + 5 = 12 is \(C^8_{12}\);
Ways to select 8 marbles so that zero red marbles is left in the jar is\(C^7_7*C^1_5\);
Ways to select 8 marbles so that zero blue marbles is left in the jar is\(C^5_5*C^3_7\);
Hence ways to select 8 marbles so that atleast one red marbles and atleast one blue marble remain in the jar is \(C^8_{12}\)- (\(C^7_7*C^1_5\)+\(C^5_5*C^3_7\)) = 495 – (5 + 35) = 455
Correct Option: D
Approach Solution (2):
Total ways to choose 12 balls = 12*11*10*9*8*7*6*5 / 8! = 495
Ways to choose all red: RRRRRRRB
By formulas would be 7*6*5*4*3*2*1*5 / 7! * 1! = 5
Ways to choose all blue BBBBBRRR = 5*4*3*2*1*7*6*5 / 5! * 3! = 35
So, final answer = 495 – 35 – 5 = 455
Correct Option: D
“There are 7 red and 5 blue marbles in a jar. In how many ways 8 marbles can be selected from the jar so that atleast one red marble and atleast one blue marble remain in the jar?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
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