a) State the fundamental principle of counting - Leaving Cert Mathematics - Question 1 - 2013
Question 1
a) State the fundamental principle of counting.
b) How many different ways are there to arrange five distinct objects in a row?
c) Peter is arranging books on a sh... show full transcript
Worked Solution & Example Answer:a) State the fundamental principle of counting - Leaving Cert Mathematics - Question 1 - 2013
Step 1
State the fundamental principle of counting.
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Answer
The fundamental principle of counting states that if one event has a outcomes and another event has b outcomes, then there are a×b different outcomes for the two events together.
Step 2
How many different ways are there to arrange five distinct objects in a row?
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Answer
The number of ways of arranging 5 distinct objects in a row is given by the factorial of the number of objects, which is calculated as follows:
5!=5×4×3×2×1=120
Step 3
Peter is arranging books on a shelf. He has five novels and three poetry books. He wants to keep the five novels together and the three poetry books together. In how many different ways can he arrange the books?
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Answer
To solve this problem, we can think of the five novels as one block and the three poetry books as another block. Therefore, we have two blocks to arrange. The number of ways to arrange the two blocks is:
2!=2
Within each block, the novels can be arranged in:
5!=120
The poetry books can be arranged in:
3!=6
Thus, the total number of arrangements is:
2!×5!×3!=2×120×6=1440
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