How many distinct arrangements of the letters in MANANGATANG are
there in which the first two letters include an M or a T (or
both)?
Note:
- MANANGATANG has 11 letters (one M,
one T, two Gs, three Ns and four As).
- These are all the possible positionings of T and M in the
first two positions:
M
M
T
T
M
T
T
M
PLEASE SHOW FULL LEGIBLE WORKING.
1a. How many arrangements are there of all the letters in
INDIVIDUAL?
1b. How many arrangements of the letters in INDIVIDUAL have all
three I’s adjacent?
1c. How many arrangements of the letters in INDIVIDUAL have no
I’s adjacent?
a) How many arrangements are there of the letters of the word
FEEBLENESS?
(b) What is the probability that if the letters are arranged at
random four E’s will be together?
(c) In a random arrangement, what is the probability that
exactly three E’ s will be together?
a) How many arrangements are there of the letters of the word
FEEBLENESS?
(b) What is the probability that if the letters are arranged at
random four E’s will be together?
(c) In a random arrangement, what is the probability that
exactly three E’ s will be together?
a) How many arrangements of all the letters in AABBCCD starts
with A but does not end with A?
b) Find the number of arrangements of all the letters in AABBCCD
in which none of the patterns AA, BB or CC occurs.
Consider arranging the letters of FABULOUS.
(a). How many different arrangements are there?
(b). How many different arrangements have the A appearing
anywhere before the S (such as in FABULOUS)?
(c). How many different arrangements have the first U appearing
anywhere before the S (such as in FABULOUS)?
(d). How many different arrangements have all four vowels appear
consecutively (such as FAUOUBLS)?
I am stuck with b , c and d
Suppose we want to choose 6 letters, without replacement, from
14 distinct letters.
(a)
How many ways can this be done,
if the order of the choices is not relevant?
(b)
How many ways can this be done,
if the order of the choices is relevant?
1. How many four-letter arrangements can be made from 10 letters
if repetitions are NOT allowed?
2. How many four-letter arrangements can be selected from 10
letters?