Fundamental Principles of Counting Flashcards
In how many ways a mobile lock password of 4 digits can be made when repetition of the digit is allowed?
- Remember the there are 10 digits as a sample i.e 0-9
Find the term independent of x in the binomial expansion [ x,4 + 2, x]^10
5th term
In how many ways a team consisting of 3 boys and 2 girls can be made from 5 boys and 5 girls?
100.
In how many ways a team consisting of 3 boys and 2 girls can be made from 5 boys and 5 girls?
- Using The combination formula C(n, r) = n! / (r! * (n - r)!)
Find the number of numbers between 1001 and 2000 which are divisible by 10. (Hint: 0 cannot come in thousand places, we can use only 1 in the thousands place and 0 in once place).
100
In an examination, a student has to attempt any seven questions out of 10. However, questions 1 & 5 are compulsory to attempt. In how many ways the student can answer the seven questions?
6720 ways
The number of terms in the expansion of binomial expression (2p – 3q)7 are:
8
The middle term of the binomial expression (2p – 3q)8 is:
90720
In an office, there are 13 male employees and 8 female employees. In how many ways the MD can select one male and one female candidate for the post of the team leader?
104 ways
The 3rd term of the binomial expression (2p – 3q)8 is:
1303668 p6q2
If nC10 = nC8, then n is equal to:
18
How many 4-digit numbers can be formed using the digits 0, 2, 3 & 1 which are divisible by 2 and repetition of digits is not allowed?
10
In how many ways letters of the words “MOUSE” can be arranged such that the vowels always remain together?
36 ways
How many words can be made using the letters of the words “KEYBOARD” with or without meaning?
40320
In a multiple-choice question test, there are 5 questions and each question has 4 answers. The number of ways a student can answer these questions is
Using exponential notation, we can write this as:
4^5 = 1024
