i). in how many ways 12 students may be equally divided into three groups?
a).5577 b).5757
c).5775 d).7755.
ii). find the number of ways in which 12 mangoes may be equally divided among 3 boys?
a).34650 b).36450
c).35650 d).34560.
intermediate(ipc)course (no) (1460 Points)
27 April 2012i). in how many ways 12 students may be equally divided into three groups?
a).5577 b).5757
c).5775 d).7755.
ii). find the number of ways in which 12 mangoes may be equally divided among 3 boys?
a).34650 b).36450
c).35650 d).34560.
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 27 April 2012
5775 is the answer First we give the three groups separate identities A,B,C. For A we have to choose 4 students from 12. This can be done in 12C4 ways i.e. 495 ways. Now we choose 4 students for group B from 8 remaining students. This can be done in 8C4 ways i.e. 70 ways. Therefore total number of ways is 495×70 ways i.e. 34650 ways. But in the original question groups are indistinguishable. Hence we should divide 34650 by 6 (the number of ways 3 things can be placed in 3 places) 34650/6 = 5775. In the second problem the three boys are distinct so the number of ways is 34650. E.g. take a simpler problem 6 students to 3 groups. let the students be denoted by 1,2,3,4,5,6. Now if we allocate them to groups A,B,C then
1st allocation: A:1,2 B:3,4 C:5,6
2nd allocation A:3,4 B:5,6 C:1,2
If we remove the labels A,B,C the above allocations are identical as in they divide the students into same groups. however in the second problem the three boys are distinct and number of ways will be 34650
intermediate(ipc)course
(no)
(1460 Points)
Replied 27 April 2012
thank you.................................
Anindya Sengupta
(Student)
(22 Points)
Replied 28 April 2012
Q. Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7:9. If each saves Rs. 50 per day, their daily income in Rs. are -
(a) (40,50)
(b) (50,40)
(c) (400,500)
(d) none of these
The answer given for this quetion is (c). But how?
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 28 April 2012
let the earnings of first person be 4x then the earnings of second person will be 5x (ratio is 4:5)
let the expenses of first person be 7y then the earnings of second person will be 9y (ratio is 7:9)
4x-7y = 50;
5x-9y = 50;
two simultaneous equations in two variables
subtracting 1st from 2nd you get x-2y =0;
i.e. x=2y;
substituiting it in the 1st equation gives x=100,y=50
therefore the answer is 400,500
Anindya Sengupta
(Student)
(22 Points)
Replied 02 May 2012
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 03 May 2012
Swapnil madhu
(Student)
(21 Points)
Replied 01 September 2016
Why we will subtract 1200 from 80000??
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