Mathematics Ext 1
Perfecting Permutations and
Combinations I
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Mathematics Extension 1: Permutations and Combinations I
Question 1
(a)
(i)
How many three digit numbers can be formed from the digits 2, 3, 4, 5
1
and 6, with no repetition?
(b)
(c)
(ii)
How many of them are less than 500?
1
(i)
How many 8 digit phone numbers are possible with the first digit 9?
1
(ii)
How many of them do not contain a 0 but contain 6?
1
How many 4 digit PINs start and end with the same digit?
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(d)
Mathematics Extension 1: Permutations and Combinations I
In how many ways can the letters of the word EQUATION be arranged if:
(i)
The word starts with an E and ends with an N?
1
(ii)
The word has E somewhere to the left of N?
1
(iii)
The consonants are together?
1
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(e)
Mathematics Extension 1: Permutations and Combinations I
Eight people form two queues of four. How many ways can this be done if:
(i)
There are no restrictions?
1
(ii)
Bob and George must stand in the same queue?
1
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(f)
Mathematics Extension 1: Permutations and Combinations I
Five car owners can choose from five mechanics.
(i)
How many different ways can they choose if there are no restrictions?
1
(ii)
If a maximum of two car owners can go to a mechanic, how many ways
2
are there?
(g)
Prove that
=
+
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.
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Mathematics Extension 1: Permutations and Combinations I
Question 2
(a)
Find the number of permutations of the word:
(i)
SNEEZE
1
(ii)
WAGGAWAGGA
1
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(b)
Mathematics Extension 1: Permutations and Combinations I
How many ways can the word SHOWS be arranged in a line
(i)
Without restriction?
1
(ii)
The S’s are together?
1
(iii)
The S’s are separated?
1
(iv)
H is before W?
1
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(c)
Mathematics Extension 1: Permutations and Combinations I
How many five letter words can be formed from the letters of the word
2
STRESS?
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(d)
(i)
Mathematics Extension 1: Permutations and Combinations I
How many ways can the word TRANSITION be arranged so that the N’s
1
are on the ends?
(ii)
How many ways can the word TRANSITION be arranged so that the N’s
2
are not on the ends?
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(e)
How many ways can
Mathematics Extension 1: Permutations and Combinations I
P’s,
to each other? Assume that
Q’s and
+1≤
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R’s be arranged so that P’s are not next
3
+ .
10