Advertisements
Advertisements
Question
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
Advertisements
Solution
These conditions are satisfied exactly when we do as follows:
First paint the central triangle in any one of the three colours.
Next paint the remaining 3 triangles, with any one of the remaining two colours.
By the fundamental principle of counting
This can be done in 3 × 2 × 2 × 2 = 24 ways.
APPEARS IN
RELATED QUESTIONS
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many numbers between 100 and 1000 have 4 in the units place?
How many numbers between 100 and 1000 have the digit 7 exactly once?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?
In how many ways 5 persons can be seated in a row?
A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if repetition of digits allowed
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is allowed
Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are not allowed?
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are allowed?
To travel from a place A to place B, there are two different bus routes B1, B2, two different train routes T1, T2 and one air route A1. From place B to place C there is one bus route say B1, two different train routes say T1, T2 and one air route A1. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
How many strings can be formed using the letters of the word LOTUS if the word neither starts with L nor ends with S?
Find the value of 6!
Find the value of 3! – 2!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
Choose the correct alternative:
The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is
Choose the correct alternative:
The number of 10 digit number that can be written by using the digits 2 and 3 is
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______
How many numbers are there between 99 and 1000 having 7 in the units place?
There are four bus routes between A and B; and three bus routes between B and C. A man can travel round-trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, in how many ways can he make round trip?
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
The number of different four-digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is ______.
Three letters can be posted in five letterboxes in 35 ways.
There will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It is being given that the balls of the same colour are identical.
