Miscellaneous Examples (NCERT) - Permutations and Combinations Video Lecture | Mathematics for Grade 11

hello friends this video on combination
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watching this video you should have
watched combination part 1 and part 2
videos let's take one more example where
both permutation and consciousness so
here the question is harmony words with
or without meaning each of three bubbles
and two consonants can be formed using
work the only for solving let's first
differentiate between other self
constant I is verbal and vol.2 T this is
the scenario we have four consonants and
what words each now the question is how
many words three vowels and two constant
that means from vowels we have to select
three consonants we have select two and
then we have to form a word so this is
and because we are selecting creating a
five letter word so we will say 4 C 3
into 4 C this is for vowels and this is
what constant number of selection so
this is number of selection now once he
is selected the alphabets we can
rearrange because it's talking about the
number of the way the number of
different ways the number of different
words that can be formed so we have to
arrange this now as we notice that 3
plus 2 there five-letter words the
number of ways we can arrange a fine
introvert is 5 for addition
that's why arrange 5 permutation so
total answer is you select first you
select first and then you multiply
arrange so what you get is 4 C 3 divorce
you 2 into 5 permutation so this is the
answer and even you solve this it says
for C 3 is equal to more than 4 this is
for completion by
Foundation is for competition back to
repetition a two-digit into five
condition is equal to 4 into Lewis's
only into 3 into 2 condition bond to oil
into 6 into 5 nutrition and this comes
out to be 2 8 8 I hope you got to find
what we have done here is we have first
than the selection so this is the number
of ways we can select from for vowels we
selected three from four consonants you
set it to and then we have arranged this
since there are five letters we arranged
in five permutation so total is
selection into arrangement let's take
one more example where we have both
Foundation and combination so in this
example we have a for girls for girls in
seven voice how many bees team of five
can be selected if it has no no girl
that means fibers that means from this
we need to select five boys because it
over five Boyle 0 1 this can be done in
from from girls who are taking 0 and
from 7 boys you are digging by so this
is one actually because it doesn't have
any meaning speaking English so this is
equal to 7 see this is one not a second
second you are saying there is no girl
or do you take anything at least one boy
and one girl so when I see at least one
boy and one girl
I can have one boy or girl or I can have
two boy speaker 3 boy so two point three
girl 3.2 girl and four boy one there are
four possible sets so then you say one
boy for girl number of boils 7 so from 7
year selecting one into it you are
selecting for girls or see this is 1 and
for this it will be 7 C 2 into 4 C 4 3
boys from 7 who is viously to three boys
and from four words viously to do with
us similarly for from 7 boys we are
selecting for boys and from
holder's definitely one you add all this
thing and all this thing in it
the answer is you add all this thing
because this is one possible scenario
one possible scenario one possible so
when I read this I read this like this
one boy and four girl 1 boy and poor
girl or so it is plus 2pi and regal -
boy and three girls or again Hana three
boy - girl three boy - girl three boy
and Google or four boy and one girl
poor boy and that's why we add this so
you add all this thing you matter
let's solve part three waited at least
three girls and you say at least three
girls so it can be three girls plus two
boy or four girl plus t1 right we'll go
ahead and because the total number of
girls is for only we can have more than
for us there isn't maybe not even
failure because this in the main side we
have only furthers they only Ferber's so
at the max we can select for us and in
the question they have answered at least
three girls so we have only two possible
completion so the answer will be for
three girls we say for c3 and two boys
swim and c2 or that is plus four words
for seafood into seven C 1 because this
is 1 here and this is them I will solve
some more examples so in this example
we'll find the N of protein dick sorry
so this is a tricky example so please
see this pay attention so the question
here is there is a word called again and
here note a and a are repeated so we
have to find what is the four so we need
know in dictionary everything is
alphabetical the first word would be
something like a a a b c d ugh it will
be the first one second guard will be
something like a G and the last word to
keep flowing
this is our dictionary is this fashion
we know this
so first let's find the number of words
that start with a so number for the
start with a is you take one a constant
here what you have left is G so the
number of possible combination you can
make from G is for completion there are
four words the number of possible a word
that starts with the letter left this a
a since a is repeated the number of
possible ways is for permutation but to
permutation because a is visited twice
as they've seen from n information
appeal implementation so it is too early
similarly for C this was for G a G this
for $5 fine for I but I we have a a G
and so here also since a is a period
twice we will get for combination by two
facility now that means total is 48 so
till 48 a G and I is consuming so 49th
word should be n a a G by this should be
49 because we have now taking words we
start with and because Agni is already
consumed the only letter left is N and
we'll arranged alphabetically a AJ this
is a 49 word now for 50th word UTV e IG
this is a deal we'll just swap this
that's why it works in dictionary it's
trying to maintain them alphabetical
order
this is the 58th but I'll explain this
question once again because it's you to
be pushing we have to find the th but in
declaring so in dictionary you know that
everything is alphabetically ordered the
first word will be e agin a b c d e f g
h i j k l h ng h i and as for second
word they'll swap this then they get na
keep going in last word will be totally
love this anymore so first we try to
find all the number of word has start
with a is 24 then g 212
in the night 12 then we found them by 48
all a gene is consumed the only letter
remaining is n we will create the first
word that can be created using letter n
that is any eg8 that should be fortunate
because 48 is already consumed and then
there's fam this to get them to you so
if you are talking about one then we
have to again move this will take two
more cushion foundation so this is the
question means seven number digits that
can be formed using desert one to zero
sorry two for two just wrote this
because I wanted to write the integral
this is the seven digit two three four
five six seven seven is it from this you
want to find so and we know that this
number 0.26
this will be something like this - this
is the range because they're talking
about seven digit number written in this
the maximum seven is number of this so
the numbers written this in this so
let's try call the number number begins
with one so when you say number begins
with one the number remaining is number
beginning with 1 so we have 1 2 3 1 2 3
4 5 6 6 possible numbers so say 6
permutation / since 2 & 4 are repetitive
2 is a period three times and four is
two times so it is six permutation by
three permutation into two permutation
it comes out to be 60 the number of
numbers that begins with two so they
said to is fix so what is left is 1 2 is
fixed what is left for us we want to do
0 right so again this will be 6
combination divided by 2 is twice -
permutation into 2 combination for is
twice so it comes out to be 180 the
number of letters that begins with 0 is
0 because there is no letter will become
0
the number that becomes with 4 is you
take for the set we have is this because
1/4 is gone so in this case the number
is 6 formation by
three permutation because too easy
detect rise this comes out to be 120 the
total number is you add there's there's
this this is equal to 60 plus 180 plus
one right and that is 360 answer let's
take the last problem the second problem
so this in this problem we have five
girls and three boys are supposed to be
seated so that no two boys are together
so in such case when we say no two boys
have together so we'll first put the
girls because no two guys that whether
we say girls one girl to go three equal
work on five they're five girls right
now we have space 1 2 3 4 5 6 so we have
6 different place where we can put the
curve because we put boys in all this
space that make sure that no two boys
them together because we are putting
girls in between so number of possible
ways of putting guys is 6 P this is the
number in which this girl's this boys
can be put together now this is
selection mom now we talk about the
arrangements once we have this done this
girl's G 1 G 2 G 3G 4 this is for the
boys right because we're talking about
arrangement so we have taken permutation
or combination here and now we have
talking about girls we can arrange this
into five permutation simple the total
lives 5 permutation into 6 e and this is
f o what my thanks thank you
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