Advertisements
Advertisements
प्रश्न
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
Advertisements
उत्तर
Either starts with L or ends with S
| L |
The first box is filled with the letter L.
The second box can be filled with the remaining letters O, T, U, S in 4 ways.
The third box can be filled with the remaining letters excluding L and the letter placed in box 2 in 3 ways.
The fourth box can be filled with the remaining letters excluding L and the letters placed in a box – 2 and box – 3 in 2 ways.
The fifth box can be filled with the remaining one letter excluding L and the letters placed in a box – 2 and box – 3, box – 4 in 1 way.
Therefore, by fundamental principle of multiplication
The number of words start with L is = 1 × 4 × 3 × 2 × 1 = 24
| S |
Since the word ends with S, the fifth box can be filled in one way with the letter S.
The remaining four boxes can be filled 4 × 3 × 2 × 1 way.
Therefore, the number of words ending with S = 4 × 3 × 2 × 1 × 1 = 24
Number of words starting with L and ends with S:
The first box can be filled with L in one way
The Fifth box can be filled with S in one way second box,
The Third box and fourth box can be filled in 3 × 2 × 1 ways with the remaining letters O, T, U.
∴ Number of words starting with L and ends with S = 1 × 3 × 2 × 1 × 1 = 6
Therefore, by fundamental principle of addition
Number of words either starts with L or ends with S = 24 + 24 – 6 = 48 – 6 = 42
APPEARS IN
संबंधित प्रश्न
How many numbers between 100 and 1000 have the digit 7 exactly once?
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?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
In how many ways 5 persons can be seated in a row?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is not allowed
How many three-digit numbers are there with 3 in the unit place?
without repetition
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 not allowed
Count the numbers between 999 and 10000 subject to the condition that there are no restriction
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 neither starts with L nor ends with S?
Count the total number of ways of answering 6 objective type questions, each question having 4 choices
Find the value of 3! × 2!
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
Choose the correct alternative:
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______
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.
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
