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
Total number of password using all alphabets -Total
number of password using no symmetric alphabets
= (26 x 25 x 24 ) - (15 x 14 x 13 )
= 12870
Three numbers can be selected and arranged out of 10 numbers in 10P3 ways 10!/7! = 10 x 9 x 8
Now, this arrangement is restricted to a given condition that first number is always less than the second number and second number is always than the third number. Thus, three numbers can be arranged among themselves in 3! ways.
Hence, required number of arrangement = (10 x 9 x 8)/(3 x 2)
= 120 ways
Number of ways of selecting one or more friends from 5 friends
= 5C1 + 5C2 + 5C3 + 5C4 + 5C5
= 5 + 10 + 10 + 5 + 1
= 31 ways
Number of ways of selecting one or more friends from 4 friends = 4C1 + 4C2 + 4C3 + 4C4
= 4 + 6 + 4 + 1
= 15 ways
? Total number of ways = 31 + 15 = 46 ways
The required number of words is : (2C1 x 4C2 + 2C2 x 2C1) 3! = 96
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
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
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.
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
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
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