If \(^{n}C_{12} = ^{n}C_{8}\), then \(n\) is equal to
20
12
6
30
The number of possible outcomes when a coin is tossed 6 times is
36
64
12
32
The number of different four digit numbers that can be formed with the digits 2, 3, 4, 7 using each digit only once is
120
96
24
100
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is
432
108
36
18
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
60
120
7200
720
A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is
216
600
240
3125
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is
11
12
13
14
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is
105
15
175
185
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
6
18
12
9
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is
\(\binom{16}{11}\)
\(\binom{16}{5}\)
\(\binom{16}{9}\)
\(\binom{20}{9}\)
The number of 5-digit telephone numbers having at least one of their digits repeated is
90,000
10,000
30,240
69,760
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is
94
126
128
None
The total number of 9-digit numbers which have all different digits is
10!
9!
9 \times 9!
10 \times 10!
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is
1440
144
7!
\(^{4}C_{4} \times ^{3}C_{3}\)
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is
3600
3720
3800
3600