When A8 is in 2nd position A4 can occupy only 1st.
When A8 is in 3rd position A4 can occupy only 1st or 2nd.
So the number of ways in which A4 and A8 can be arranged = 1+2+...+14 = 14*15/2
In the remaining 13 positions other students can be permuted in 13! ways.
Hence total number of ways = 13! * 14*15/2 = 15!/2
Workspace
NA
SHSTTON
24
Solv. Corr.
41
Solv. In. Corr.
65
Attempted
0 M:0 S
Avg. Time
44 / 100
Choose the correct option.
In how many ways can the letters of the word "BANKING" be arranged, such that vowels do not come together?
Total no. of words = 7!/2!=2520
Total no. of words in which vowels together = bnkng(ai)
=(6!/2!)*2!=720
So, the number of words in which vowels do not come together = (2520 - 720) = 1800
Workspace
NA
SHSTTON
11
Solv. Corr.
23
Solv. In. Corr.
34
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Avg. Time
45 / 100
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A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behin The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
Two tallest boys can be arranged in 2! ways, rest 18 can be arranged in 18! ways.
Girls can be arranged in 6! ways.
Total number of ways in which all the students can be arranged = 2! * 18! * 6! = 18! *1440
Workspace
NA
SHSTTON
14
Solv. Corr.
25
Solv. In. Corr.
39
Attempted
0 M:0 S
Avg. Time
46 / 100
Choose the correct option.
The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
The order of each letter in the dictionary is ABLORU.
Now, with A in the beginning, the remaining letters can be permuted in 5! ways.
Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways.
With L in the beginning, the first word will be LABORU, the second will be LABOUR.
Hence, the rank of the word LABOUR is 5!+5!+2 =242
Workspace
NA
SHSTTON
10
Solv. Corr.
18
Solv. In. Corr.
28
Attempted
0 M:0 S
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47 / 100
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In how many possible ways can write 3240 as a product of 3 positive integers a,b and c.
We have to distribute three 2's to a, b, c in 3+3−1C3−1 = 5C2 = 10 ways
We have to distribute four 3's to a, b, c in 3+4−1C3−1 = 6C2 = 15 ways
We have to distribute one 5 to a, b, c in 3 ways.
Total ways = 10*15*3 = 450 ways
Workspace
NA
SHSTTON
11
Solv. Corr.
25
Solv. In. Corr.
36
Attempted
0 M:0 S
Avg. Time
48 / 100
Choose the correct option.
In how many ways can the letters of the english alphabet be arranged so that there are seven letter between the letters A and B, and no letter is repeated
We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
These 18 letters are arranged in 18! ways.
So Answer is 2 x 24P7 x 18!
OR 2 x 24P7 x 18! = 36 x 24!.
Workspace
NA
SHSTTON
8
Solv. Corr.
12
Solv. In. Corr.
20
Attempted
0 M:0 S
Avg. Time
49 / 100
Choose the correct option.
How many different integers can be expressed as the sum of three distinct numbers from the set {3, 8, 13, 18, 23, 28, 33, 38, 43, 48}?
A owes B Rs.50. He agrees to pay B over a number of consecutive days starting on a Monday, paying single note of Rs.10 or Rs.20 on each day. In how many different ways can A repay B.
He can pay by all 10 rupee notes in 5 days = 1 way
3 Ten rupee + 1 twenty rupee = 4!/(3!*1!) = 4 ways
1 Ten rupee + 2 twenty rupee notes = 3!/(2!*1!) = 3 ways
Total ways = 1 + 4 + 3 = 8
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