Question

3. How many different signals can be generated from
6 flags of different colours if each signal makes use of
all the flags at a time, placed one below the other?
4. Seven songs are to be rendered in a programme. In how
many different orders could they be rendered ?
5. There are 6 items in column A and 6 items in column B.
A student is asked to match each item in column A with
an item in column B. How many possible answers (correct
or incorrect) are there to the question ?
6. (i) How many three-digit numbers are there, with
no digit repeated ?
(ii) How many four-digit numbers are there, with
no digit repeated ?
(ii) How many natural numbers from 1 to 1000
have none of their digits repeated ?
7. How many even numbers of three digits each can be
made with the digits 1, 2, 3, 4, 5, 6, if :
(1) no digit is repeated (ii) digits can be repeated ?
8. Find the number of 4-digit numbers that can be formed
using the digits 1, 2, 3, 4, 5 if no digit is used more than
once in a number. How many of these numbers will be
even ?
(N.C.E.R.T.)​

Answer 1

Answer:

6 different signals can be generate

Answer 2

Answer:

3)1956

4)5040

5) 720

6)i)648

ii)4537

iii)738

7)i)60

ii)108

8)49

Step-by-step explanation:

3)Number of signals using one flag = 6P1 = 6 Number of signals using two flags = 6P2 = 30 Number of signals using three flags = 6P3 = 120 Number of signals using four flags = 6P4 = 360 Number of signals using five flags = 6P5 = 720 Number of signals using all six flags = 6P6 = 720 Therefore, the total number of signals using one or more flags at a time is 6 + 30 + 120 + 360 + 720 + 720 = 1956

5)Number of arrangements of n things taken all at a time

{∵ 0! = 1}

= 6 × 5 × 4 × 3 × 2 × 1

= 720