Riya invests a part of Rs. 42,000 in 9% stock at Rs. 120 and the remainder in 15% stock at Rs. 110. If her total dividend per annum is Rs. 4500, how much does she invest in 15% stock at Rs. 110?
An alphanumeric character is randomly selected from following sentence:
"Ultimately, education in its
real sense is the pursuit of truth.
It is an endless journey through
knowledge and enlightenment."
What is the probability that picked character is one of the following letters C or P or V or E or S?
Note: Alphanumeric character means alphabet or number. Space and other characters should be ignored.
Let's first find out the number of arrangements without any restrictions. The word 'CHIMPANZEE' has 10 letters where E occurs 2 times.
Therefore, number of ways in which the letters of the word 'CHIMPANZEE' can be arranged without any restrictions = 10!/2! = 1814400
Now let's find out the number of arrangements where all the vowels come together. The word 'CHIMPANZEE' has 10 letters where 4 are vowels (I, A, E, E).
Vowels must come together. Therefore, group these vowels and consider it as a single letter.
i.e., CHMPNZ, (IAEE)
Thus we have total 7 different letters.
Number of ways to arrange these 7 letters = 7! = 5040
In the 4 vowels, E occurs 2 times.
Number of ways to arrange these 4 vowels among themselves = 4!/2!=12
Therefore, number of ways in which the letters of the word 'CHIMPANZEE' can be arranged where all the vowels come together =5040×12=60480
Number of ways in which the letters of the word 'CHIMPANZEE' can be arranged where all the vowels never come together= 1814400 − 60480
= 1753920
Option 3)