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?
How many distinct arrangements of the letters in MANANGATANG
have no A’s in the first six places?
NOTE: MANANGATANG has 11 letters, so the last five places must
have four A's and one other letter.
PLEASE SHOW FULL LEGIBLE WORKING.
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.
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?
How many arrangements of length n where 1 ≤ n ≤ 8 can be formed
from the letters A, A, B, C, C, C, D, E where
(a) both A’s are adjacent?
(b) the string starts or ends with A?
(c) you use (exactly) 4 letters from the list?
a) How many
four-letter words can be formed from the letters of the word
LAUNDRY if each letter can only be used one time in a word? Y is
NOT considered a vowel in this word.
b) How many contain the letter
Y?
c) How many contain both
vowels?
d) How many of them contain
exactly three consonants?
e) How many of them begin and end
in a consonant?
f) How many begin with
N and end in a vowel?
g) How many begin with N and...
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?