Question:
Four Rupee 5 coins, three rupee 2 coins and two rupee 1 coin are stacked together in a column at random. The probability that the coins of the same denomination are consecutive, is
Four Rupee 5 coins, three rupee 2 coins and two rupee 1 coin are stacked together in a column at random. The probability that the coins of the same denomination are consecutive, is
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Count all arrangements of the identical coins, then treat each denomination as one block.
Updated On: Nov 12, 2026
- \(\frac{13}{9!}\)
- \(\frac{1}{210}\)
- \(\frac{1}{35}\)
- \(0\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Coins of the same denomination are identical, so we count arrangements of a multiset.
Step 2: Total arrangements
There are 9 coins: 4, 3 and 2 of three kinds. The total number of stackings is \(\dfrac{9!}{4!\,3!\,2!}=1260\).
Step 3: Favourable arrangements
Each denomination forms one block, so we arrange 3 blocks in \(3!=6\) ways.
Step 4: Probability
\(P=\dfrac{6}{1260}=\dfrac{1}{210}\)
Final Answer:
The probability is 1/210. \[ \boxed{\text{(B) }\dfrac{1}{210}} \]
Coins of the same denomination are identical, so we count arrangements of a multiset.
Step 2: Total arrangements
There are 9 coins: 4, 3 and 2 of three kinds. The total number of stackings is \(\dfrac{9!}{4!\,3!\,2!}=1260\).
Step 3: Favourable arrangements
Each denomination forms one block, so we arrange 3 blocks in \(3!=6\) ways.
Step 4: Probability
\(P=\dfrac{6}{1260}=\dfrac{1}{210}\)
Final Answer:
The probability is 1/210. \[ \boxed{\text{(B) }\dfrac{1}{210}} \]
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