Fundamental Principle of Counting Video Lecture | Mathematics (Maths) Class 11 - Commerce

all right this final video in the series
for this unit on probability will be on
using what we call the fundamental
counting principle this is another
really helpful tool in mathematics when
whenever we're trying to determine the
total possible outcomes for compound
events as we learned earlier that
compound events are more than one event
happening so we're trying to figure out
how many total possible outcomes would
happen and the fundamental counting
principle says that the total possible
outcomes of compound events is found by
multiplying the number of outcomes for
each event so if I have three different
events I'm going to see how many
outcomes I have for the first event
multiply that by how many outcomes I
have for the second event multiply that
by how many outcomes I have for the
third event alright and if I had more
events I'd keep on doing the same exact
thing all right and that would give me
the total possible outcomes I should
have and then I can list the outcomes
separately as we did in our in our
previous video on listing the possible
outcomes alright for compound events all
right so but in this video all we're
trying to do is determine how many not
what are the outcomes alright let's go
to some problems to see how this works
all right you flip a coin flipping a
coin and spin the spinner so those are
two different events how many outcomes
are possible well flipping a coin how
many outcomes do you have there - it's
heads or tails and then how many
outcomes you have for spinning the
spinner let's count one two three four
five different outcomes so how many
total possible outcomes do I have well
it's 2 times 5 which is 10 possible
outcomes ok and being precise I wouldn't
just write 10 I'd write 10 possible
outcomes all right and then if I were
asked but this is not the task if I were
asked what
are the outcomes then I would look at
the first event what are the outcomes
for the first event heads or tails how
many outcomes arrive for the next event
five so I drop five separate branches
and then I'd list them let's see I have
eight four five six seven eight four
five six seven and then I'd list them
out H - H H - eight H - 4 H - 5 8 - 6 H
- 7 T - 8 T - 40 - 50 - 60 - 7 and those
will be my outcomes and if you can see
there are ten of them one two three four
five six seven eight nine ten possible
outcomes all right though this task is
just determining how many okay don't
list them unless you're told to list the
outcomes or ask what are the outcomes
let's go to the next one you pick a
marble and you roll a die all right how
many outcomes are possible well look at
the marble this is your first event how
many outcomes one two three four and
look at your die if you really die there
are six different sides so you can land
on six different sides and whenever
you're determining outcomes you multiply
because if you look at your if your tree
diagram you'll see that you're actually
just multiplying whatever you get here
by that number so 4 times 6 is 24 answer
is 24 possible outcomes
notice how this fundamental counting
principle helps us to get the answer
very quickly as opposed to having to go
through every single drawing to figure
it out and then count later it's a quick
way nice math tool to help us alright
next you do the next problem and see if
you cannot see if you can do this on
your own and come back when you have the
answer alright you pick a marble and you
roll a die those are two different
events how many outcomes are possible
alright so whenever I see this I'm using
the fundamental counting principle as a
two
one two three four five for my first
event of rolling a mark picking a marble
and rolling a die outcomes are six five
times six is thirty so I have 30
possible outcomes and the last one
doesn't involve any pictures so we have
to have we have to make sense of this
problem as we go through and persevere
in solving it hunter wants to buy a new
pair of skates all right so far nothing
there I just know hunter wants to go
shopping for some skates
he can buy speed skates figure skates or
hockey skates all right a pair of skates
can come in blue or silver and can be
decorated with blue streaks or green
clovers how many different combinations
can hunter choose from well first I
figure out what are my different events
here he can Hunter wants to buy a new
pair of skates yes I know he wants to
buy skates
great he can buy speed skates figure
skates or hockey skates so right here I
guess this first event is is type of
skate and how many do I have speed
skates one figure skates two hockey
skates three so three different types of
skates next event a pair of skates can
come in blue or silver all right so this
is color blue is one two is silver so
two different colors and can be
decorated so these are decorations with
blue streaks one or green clovers - all
right so I know that there are two
different outcomes for decorations how
many different outcomes can enter choose
from I multiply 3 times 2 is 6 times 2
is 12 so there are 12 different outcomes
whenever you're asked how many different
outcomes or how many possible
combinations uh can happen you will
always use what we call the fundamental
counting principle or the FCP okay all
right hope you add that to your toolbox
bye-bye