Permutations & Combinations
IB Mathematics AA · SL & HL · Shadow Worksheet
Practice
Question 1
Evaluate:
(a)\(^6P_3\)
(b)\(^8C_3\)
(c)\(\dfrac{7!}{4!}\)
(a)
Answer
\(6 imes5 imes4=120\)
(b)
Answer
\(\dfrac{8!}{3!\,5!}=56\)
(c)
Answer
\(7 imes6 imes5=210\)
Question 2
How many ways can 5 different books be arranged on a shelf?
Question 3
A committee of 3 is chosen from 8 people. How many committees are possible? How many if a particular person must be included?
All committees
\(inom{8}{3}=56\)
One fixed person
Choose 2 from remaining 7: \(inom{7}{2}=21\)
Answer
56 total; 21 with the fixed person
Question 4
How many 4-digit numbers greater than 5000 can be formed using the digits 3, 5, 6, 7, 8 without repetition?
First digit must be 5, 6, 7, or 8 (4 choices)
Remaining 3 digits from 4 remaining: \(4 imes4 imes3 imes2=96\)
Question 5
In how many ways can 4 boys and 3 girls sit in a row if all the girls must sit together?
Treat girls as one block
\(5!\) arrangements of 5 entities, \(3!\) arrangements within the block
Answer
\(5! imes3!=120 imes6=720\)
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