IIT JEE , AIEEE Forum - Mathematics , Algebra - Permutations:In how many ways can 4 ppl be selected out of 10 ppl,such none is selected co

AJ1991

Permutations:In how many ways can 4 ppl be selected out of 10 ppl,such none is selected consecutively.

AJ1991

plz answer someone.rates assured.

akhil_o

what do u mean by selected consecutvly?

AJ1991

i.e.eg:

If first is selected ,second cannot be selectd.

Answer given is 7C3,but how??

AJ1991

Come on answer!!

AJ1991

plz answer someone..

priyesh

ans is 7C4

bcoz let the 6 persons not selected be seated

so the four selected persons can be seated in between the seven gaps

so no. of ways of selecting four gaps out of 7 = 7C4 = 35

sboosy

let 1 2 3 4 5 6 7 8 9 10 represent the persons

Consider the case

1 3 5 :

the fourth person can be 7 or 8 or 9 or 10 = 4 cases

1 3 6:

we get 3 cases

1 3 7

we get 2 cases

1 3 8

we get 1 case

so total = 10

now

1 4 6

we get 3 cases

1 4 7

2 cases

1 4 8

1 case

so total = 6

like this if we go we get

(4+3+2+1) + (3+2+1) + (2+1) + 1 = 20

but this is only starting with 1

now with 2 we will get another sequence

(3+2+1) + (2+1) + 1 = 10

now with 3 we get

(2+1) + 1 = 4

with 4 we get only one that is 4 6 8 10

= 1

so answer is

20 + 10 + 4 + 1 = 35 = 7C₃

priyesh

thats a very lengthy method the one which i've given is the shortest

i'll explain it a bit more clearly

since there is no condition on the persons not selected therefore let us place them first

Let the persons not selected be A,B,C,D,E,F

_A_B_C_D_E_F_

therefore the persons which are selected(4) have 7 places for themselves to select therefore no. of ways of selecting 4 places out of 7 are ⁷C₄= 35 ways

In these type of questions we must place the elements having no condition on them first & then proceed further.

computer001

(4+3+2+1 +3+2+1 +2+1 +1)+(3+2+1 +2+1 +1)+(2+1 +1) +1...using recurrsions=35

Chandravadan

mr computer, what does recurrsion mean?

computer001

nothin much da..jus a fancy way of sayin tht if u actually plot a few cases on paper u'll c a pattern in the values appearin in the cases.. from tht jus get a kinda series..thts all..

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