bcafamilyPermutation and Combination
If there are 5 routes for travelling two places A and B. How many option are there for a a person to travel from A to B and return back[2015]
5
10
9
25
A school committee consists of 2 teachers and 4 students, the number of diffrent committees that can be formed from 5 teachers and 10 students are [2014]
8
10
15
2100
Out of 7 consonants and 4 words. How many word of 3 cononants and 2 vowels can be formed[2013]
25200
210
1400
1050
Find the arrangement that can be made out of the letters of the word 'MANAGEMENT'[2009]
453600
456300
45300
226800
In how many ways four persons. A, B, C, D can be arranged taking 2 person at a time[2008]
12
15
16
18
Other Questions
How many three letter words are formed using the letters of the word TIME?
12
20
16
24
4P3 = 4 x 3 x 2 = 24
Using all the letters of the word "THURSDAY", how many different words can be formed?
8
8!
7
7!
Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.
The number of different permutations of the word BANANA is
720
60
120
360
Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
3
6
24
120
The number of words = 3! = 6.
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
32
48
36
60
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
120
720
4320
2160
The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
165
185
205
225
Total number of persons in the committee = 5 + 6 = 11
11C8 = 165
In how many ways can six members be selected from a group of ten members?
8C4
10C4
10C5
10P4
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
63
90
126
45
If nPr = 3024 and nCr = 126 then find n and r.
9, 4
10, 3
12, 4
11, 4
Explanation:
Hence
24 = r!
Hence r = 4
Now nP4 = 3024
n(n-1)(n-2)(n-3) = 9.8.7.6
n = 9.
If 10Pr = 720, then r is equal to
4
2
3
1
Number of ways in which 12 different ball can be divided into group of 5,4 and 3 balls are.
12! / 5! 4!
12! / 5! 4! 3!
12! / 5! 4! 3! 3!
None of these
In how many ways can a committee of 5 made out 6 men and 4 women containing at least one women?
246
222
186
None of these
A committee of 5 out of 6 + 4 - 10 can be made in 10C5 = 252 ways
If no woman is to be included, then number of ways = 5C5 = 6
the required number = 252 - 6 = 246
If nPr = 720 nCr then r is equal to
3
7
6
4
n! / (n - r)! = 720(n!) / (n - r)!r!
r! = 720
r = 6
How many new work are possible from the letter of the word PERMUTATION?
11! / 2!
(11! / 2!) - 1
11! - 1
None of these
