Since one file is always selected, we can say that we select that particular file in 1C1 ways.
Now, the number of files that remain is 13 and we need to select 6 files from it as one is already selected. This can be done in 13C6 ways.
To get the number in which we always select a particular file and then select 6 more from the remaining, simultaneously, is given by multiplying the two quantities derived above i.e. 1C1 x 13C6
Hence, the answer to your question is:
1C1 x 13C6 = 1 x 1716 = 1716 ways.
Cistern will be filled in 24 hours
Using LCM approach:
LCM of 10, 15 and 8 = 120
Work done by pipe A in 1 hour = 12 units
By Pipe B = 8 units
By Pipe C = -15 units
Total work done in 1 hour = 12+8-15 = 5 units
Total time taken = 120/5 = 24 hours
Total arrangements of all alphabets of word PASSENGER = 9!/2!*2!
When both S are together = 8!/2!
When S are not together = 9!/2!*2! – 8!/2! = (8!*7)/4
Suppose the 3 digit number be n
Now, according to the question:
229=n*a+3 & 568=n*b+3
Subtracting both equations, we get:
568-229=n(b-a)
i.e. n(b-a)=339
It means n divides 339
But the divisors of 339 are 3, 113
Therefore, the smallest 3 digit number is 113.
The balls are numbered as 1,2,3,4,5,6,7,8,9 and 10.
If 1 numbered ball picks up by Anuj then Anisha will picks up 2 or 3 or 4 or ..... or 10 = 9 ways.
like this,
2 numbered ........................... = 8 ways.
3 numbered ............................ = 7 ways.
.
.
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9 numbered................................ = 1 way
So, number of ways that Anuj picks a ball numbered less than that picked by Anisha = 9+8+7+6+5+4+5+4+3+2+1 = 45 ways
Amit picked a ball from remaining 8 balls = 8c1 = 8 ways
one ball lesser from 3, that is 3c1
number of possible ways = (45*8)/3= 120
Total number of possible ways = 10c1 * 10c1 *10c1 = 1000
The probability = 120/1000 = 3/25