Some Probability and Permutation questions...

Question

1.  Find the number of permutations of the elements in the set {1, 3, 5, 7, 9, 11}.

a. 6                     b. 21             c. 36             d. 720

2.  If there are 9! different seating arrangements around a round table, how many people are there?

a.  9        b. 18       c. 8         d. 10

3.  How many 8 digit telephone numbers can be made from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} such that the first digit is not 0? (Repetition of a digit is allowed.)

a. 9 x 9P7   b. 10⁸      c. 9 x 10⁷    d. 79

4.  How many pin code numbers of 5 digits can be made if it does not start with the digit 0 and no digits may be repeated?

a. 27,216    b. 30,240    c. 1,360,080     d. 1,510,200

5. Find the number of 10 - digit numbers starting with 1 and ending with 0, no repetition of a digit is allowed.

a. 8        b. (10!) – 2   c. 8!      d. 2 (8!)

Answer 1

6P6=6!/(6-6)!= 6!/0! =6!/1 =6! =6x5x4x3x2x1=720

nPr = n!/(n-r)! n elements taken 6 at a time