Five persons entered in the lift cabin on the ground floor of an 8-floor house. Suppose each of them can leave the cabinindependently at any floor begining with the first. Find the total number of ways in which each of the five persons can leave the cabin
(i) at anyone of the 7 floor.
(ii) at different floors.

4

(a)

How many natural numbers less than 1000 can be formed with the digits 1, 2, 3, 4, and 5, if repetition of digits is allowed?

4

(a)

How many numbers greater than 1000, but not greater than 4000 can be formed with the digits 0, 1, 2, 3, 4, if
(i) repetition of digits is alllowed?
(ii) repetition of digits is not allowed?

4

(a)

How many different words can be formed with the letters of the word 'HARYANA'? How many of these have H and N together?

4

(a)

Prove that 35! is divisble by 2¹². What is the largest integer n such that 35! is divisible by 2ⁿ?

4

(a)

How many different words can be formed with the letters of the word 'HARYANA'? How many of these begin with H and end with N?

4

(a)

If  ²⁸C_2r : ²⁴C_2r-4 = 225 : 11 , find r

4

(a)

Evaluate ²⁰C₅ + \(\sum _{ r=1 }^{ 5 }\) ^25-rC₄ 

4

(a)

7 points lie on a circle . How many chords can be drawn by joining these points?

4

(a)

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

4

(a)