distinct permutations.............

hello,

plz try to do these questions.

(a) Find the number of distinct permutations that can be formed using the letters of the word “Mathematics”.

(b) How many integers from 1 through 1000 are multiples of 3 or multiples of 5?

Question 2:

Compute for each of the following values of x.

( a ) 20/3 ( b) -2.07

Question 3:

Two cards are drawn at random from a well shuffled pack of 52 cards. Find the probability that:

(i) one is king and other is queen.

(ii) Both are of same color.

(iii) Both are of different color.

Question 4:

A coin is biased such that a head is thrice as likely to occur as a tail. Find the probability distribution of heads and also find the mean and variance of the distribution when it is tossed 4 times.