When three dice are rolled, the number of possible outcomes = 63 = 216
Number of possible outcomes in which 2 does not appear on any dice = 53 = 125
? Number of possible outcomes in which atleast one dice shows 2 = 216 - 125 = 91
To construct 2 roads, three towns can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third road goes from the third town to the first town, a triangle is formed and if it goes to the fourth town, a triangle is not formed, So there are 24 ways to form a triangle and 24 ways of avoiding the formation of triangle.
As, there are six players, so total ways in which they can be arranged = 6 ! ways
Also, two particular players,are never together.
? Required ways = 6!/2! = 360
No of multiple choice type questions = 4
Total number of ways = 5 x 5 x 5 x 5 = 625
Number of correct answer = 1
Number of false answers = 625 - 1 = 624
Maximum number of such different groups = ABC , ABD, ABE, BCE, BDE, CEA, DEA = 7
Each question can be answered in 2 ways.
? 10 question can be answered = 210 = 1024 ways
Number of 1 digit numbers = 5
Number of 2 digit numbers = 52 = 25
Number of 3 digit numbers = 53 = 125
Number of 4 digit numbers = 54 = 625
Number of 5 digit numbers = 55 = 3125
? Total number of numbers formed with these digits
= 5 + 25 + 125 + 625 + 3125 = 3905
Total number of persons = 9
Host can sit in a particular seat in one way .
Now, remaining positions are defined relative to the host .
Hence, the remaining can sit in 8 places in 8P8 = 8! ways.
? The number of required arrangements = 8! x 1 = 8! = 8! ways
Case I :-
If lady sets on reserved seat, then
2 men can occupy seats from 4 vacant seats in 4P2
= 4 x 3 = 12 ways
Case II :-
If lady does not site on reserved seat, then 1 women can occupy a seat from seat in 4 ways, 1 man can occupy a seat from 3 seats in 3 ways, also 1 man left can occupy a seat from remaining two seats in 2 ways.
? Total ways = 4 x 3 x 2 = 24 ways
Hence, from Case I and case II , total ways = 12 + 24 = 36 ways
Required number of member played will be (139 - 1) = 138
Number of ways selecting 1 question from ex-7 = 12C1
Number of ways selecting 1 question from ex-8 = 18C1
Number of ways selecting 1 question from ex-9 = 9C1
? Total ways = 12C1 x 18C1 x 9C1 = 12 x 18 x 9 = 1944
Comments
There are no comments.Copyright ©CuriousTab. All rights reserved.