Question

1. There are 10 students in a class. How many ways can they be arranged in a line if two friends always want to stay together?

   I.             100

   II.          3,628,800

   III.       725,760

   IV.       45

   V.          90

   VI.       10

   I
   II
   III
   IV
   VI
   VI

2. There are 10 students in a class. If each student shakes hand with every other student, how many possible shake-hands have taken place?

   I.                   100

   II.                3,628,800

   III.             725,760

   IV.             45

   V.                90

   VI.             10

   I
   II
   III
   IV
   V
   VI

Answer 1

Two friends want to sit together. So, we can consider them as one person
For 9 members to sit in a line, it is 9!
II. 3,628,800

Hand shakes for 10 persons
Each one shakes hands with other 9: n(n-1)
For two persons it is considered twice. So n(n-1)/2
n(n-1)/2 = 10(9)/2 = 5*9 = 45
IV. 45