IIT JEE , AIEEE Forum - Mathematics , Algebra

amulye

d no. of ways in which any 4 letters can b selected frm d word "CORGOO" is

d no of ways of 7 digit no d no. d sum of whose digits is even

d no.of no.s smaller dan 10⁴ in d decimal notation of which all d digits r different is

mukundmadhav

q.1 3c1 + 3c2 + 3c3 = 7

mukundmadhav

q.3
9.9.8.7 + 9.9.8 + 9.9 +9

RyuAmakusa

q3 9.9.8.7

mukundmadhav

@ ryu.. it's not necessarily a 4 digit number

RyuAmakusa

oh then the ans is infinity ......but i dont know i should have noted 4 digit no. as mukund said and also i should have said infinity at the first time ....my skill has decresed i guess..

rhd92781

q2) no of such natural nos =
7 dig nos with 0 odds + 2 odds + 4odss + 6 odds (including 0 at 7th place) - 6 dig nos with 0 odds + 2 odds + 4 odds + 6 odds (including 0 at 6th place)
=5^7(7C0 + 7C2 + 7C4 + 7C6) - 5^6(6C0 + 6C2 + 6C4 + 6C6)

*not so sure

mukundmadhav

It isn't infinity dude.. Less than 10^4 means 4 digit numbers, 3 digit numbers, 2 digit numbers and 1 digit numbers. Check out my answer above

mukundmadhav

Second question looks alright to me..

RyuAmakusa

even if i ASSUME what u say is true then what about 0 is 0 not a 1 digit no.

mukundmadhav

It's not a natural number.. In number problems we generally speak only of natural numbers and not whole numbers

ashish_banga

1) = 7
there are 3Os
so when we select all the Os, no of selections of the fourth letter = 3C1
when 2 Os are selected, no. of selections of other 2 = 3C2
similarly case 3

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