Combinatronics Flashcards
a) In how many ways can 6 people sit around a circular table?
b) If seating is random, find the probability that 3 particular people will sit together.
a)120 ways
b) 1/3 or 30%
In how many ways can the letters of the word EXCEPTIONAL be arranged?
19,958,400
Find the number of ways that the letters of the place name ULLADULLA can be
arranged.
3780
A bag contains 5 balls of different colours − red, yellow, blue, green and white. In how
many ways can these 5 balls be arranged:
a) with no restrictions
b) if the yellow ball must be first
c) if the first ball must not be red or white
d) if blue and green must be together
e) if red, blue and green must be together?
a) 120
b) 24
c) 72
d) 48
e) 36
In how many ways can a set of 10 beads be arranged:
a) in a line?
b) in a circle around the edge of a poster?
c) on a bracelet?
a) 3628800
b) 362880
c) 181440
A group of 7 people sit around a table. In how many ways can they be arranged:
a) With no restrictions?
b) If 2 people want to sit together?
c) If 2 people cannot sit together?
d) If 3 people sit together?
a) 720
b) 240
c) 480
d) 144
a) How many different arrangements can be made from the numbers 3,4,4,5,6
b) How many arrangements form numbers greater than 40,000
c) How many arrangements form numbers less than 50,000?
a) 60
b) 48
c) 36
Find the Probability that an arrangement of the word LAPTOP will begin with T
1/6
A minibus has 6 forward-facing and 2 backward-facing seats. If 8 people use the bus, in how many ways can they be seated:
a) With no restrictions
b) If one person must sit in the forward-facing seat
c) If two people must sit in the forward-facing seat
a) 40320
b) 30240
c) 21600
The letters of the word THEORY are arranged randomly. Find the number of arrangements:
a) With no restrictions
b) If E is at the beginning
c) If the first letter is a consonant and the last letter is a vowel
a) 720
b) 120
c) 192
What is the minimum number of people required in a group to ensure that three are born
in the same month?
25
Solve (x − 1) ≤ (1 − x)(3 + x)
-4<=x<=1
(i) How many arrangements of the letters of the word CERTIFICATE are possible?
(ii) How many arrangements of the letters in the word CERTIFICATE are possible if
the vowels must occupy the 2nd, 3rd, 5th, 7th and 9th positions?
i) 2494800
ii) 5400
A picnic is arranged for 4 adults and 4 children at the zoo.
In how many ways can
(i) they queue at the turnstile to get in?
(ii) they sit around a picnic table if the children and the adults alternate?
(iii) each child pair with an adult to attend 4 different exhibitions?
i) 40320
ii) 144
iii) 576
How many arrangements in the word ASSESSMENT will the E’s be separated in?
60480
A closed ball contains 8 balls numbered 1,2..8
What is the probability that a selection of 3 balls at random contain only even numbered balls?
1/14
A picnic is arranged for 4 adults and 4 children at the zoo.
In how many ways can
(i) they queue at the turnstile to get in?
(ii) they sit around a picnic table if the children and the adults alternate?
(iii) each child pair with an adult to attend 4 different exhibitions?
i) 40320
ii) 144
iii) 576
Six men and four women have offered to serve on a committee of five people.
(i) How many different committees can be chosen?
(ii) How many different committees can be chosen containing at least one women?
i) 252
ii) 246
b) Find the number of ways the seven letters of the word QUARTIC can be
arranged in a line
(i) without restriction.
(ii) so that the three vowels are all next to each other but the four
consonants are not all next to each other.
i) 5040
ii) 432
