E - 1/11
M - 2/11
The letters in the word MATHEMATICS are arranged randomly.
What is the probability that the first letter is E?
What is the probability that the first letter is M?
2 answers
number of possible arrangements
= 11!/(2!2!2!) , 2 A's, 2 T's, 2 M's
= 4989600
number with E first
= 1x10!/(2!2!2!) = 453600
prob E first = 453600/4989600
= 4536/49896
= 1/11
with M first
number of arrangements
= 2x10!/(2!2!2!) = 907200
prob with M first = 907200/4989600
= 9072/49896
= 2/11
Ms Sue had both of those clearly using a very common sense reasoning
= 11!/(2!2!2!) , 2 A's, 2 T's, 2 M's
= 4989600
number with E first
= 1x10!/(2!2!2!) = 453600
prob E first = 453600/4989600
= 4536/49896
= 1/11
with M first
number of arrangements
= 2x10!/(2!2!2!) = 907200
prob with M first = 907200/4989600
= 9072/49896
= 2/11
Ms Sue had both of those clearly using a very common sense reasoning
3 answers