A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row) The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her) How many such arrangements of the 6 people are possible?
A) 5
B) 6
C) 9
D) 24
E) 36
Ans is B- 6
I got the ans as 5.
Let s1,s2,s3,s4,s5,s6 represent the 6 persons in increasing order of their heights.As desired, assignment of 6 persons in 2 rows can be obtained in following 5 ways:-
1)s4,s5,s6
s1,s2,s3
2)s3,s5,s6
s1,s2,s4
3)s2,s5,s6
s1,s3,s4
4)s3,s4,s6
s1,s2,s5
5)s2,s4,s6
s1,s3,s5
Note that s1 ans s5 needs to be fixed in their alloted positons
good work raghukiran
i think its s1 and s6 should be in fixed postions rather than s1 and s6..as said by raghu
s1 and s6 should be in fixed positins rather than s1 and s5 as said by raghu,…wat do u say raghu>>>
Yes,u r right,imtiaz.I have mistakenly typed s6 as s5.
ya its A- 5
5
Someone plz explain in a better way plz.
5
is there any better way??????? plz??????
the answer is 1.The conditions taken by raghu kiran dont satisfy the 2 conditions mentioned in the questions or kud u please xplain in detail
i came up with 5.
came up with the same method as raghu
Its 5,same as explaind by raghu
is there no short cut?
any shoter way to approach this problem ….pls help….
any smarty here ???
Ans is 5
just take 6 numbers as 1,2 ,3 ,4 ,5,6,
It will be easier to u to follow the conditions mentioned and get the answer as 5, with actual numbers it is easy and less chance of errors as compared to variables.
Answer is 5
I tried by a simple way …
First row:
1st place – only S1
2nd place – either S2 or S3
3rd place – S4 or S5
second row:
4th place – S2, S3, or S4
5th place – S5 or S4
6th place – S6
We can have 5 combinations of 2nd 3rd 4th and 5th place…
So ……….. ans 5
Is this a permutation problem…order of height is important.
6 people…choose 2 or 3?
i like zhulander’s explanation. that’s the logic i had, too. 5.
1] 4 5 6
1 2 3
2] 3 2 6
1 2 4
3] 3 4 6
1 2 5
4] 2 5 6
1 3 4
5] 2 4 6
1 3 5
Ans is 36
6 people can be divided into 3 tall and 3 short…
For the first time,
1st row 3C1
2nd row 3C1
that is 3C1*3C1=9
For the second time,
1st row 2C1
2nd row 2C1
that is 2c1*2C1=4
For the third time,
1st row 1C1
2nd row 1C1
that is 1
Therefore 9*4*1=36
correct me if i’m wrong….
I appreciate ylmson’s generalized explanation. Just imagine if u r asked the same problem with 8 ppl. Wouldn’t it be too confusing and time consuming to list down all the possible arrangements.
Anyway, the answer is 5.
my ans is 9.
if u select the persons for 1st row it is enough since after this selection ,there is only one way to fill the second row
let us take 123456 are the persons
for 1st place in row1: 1
2nd :2or3or4
3rd :3or4or5
so the probability is 1*3*3=9
ans is 5
1 LSP (Lowest significant place) which is left corner of first row.while 6 has to be fixed at MSP(most significant place) right corner of second row.
we have 5 possibilities
456 356 346 256 246
123 124 125 134 135
I think it’s 36.
Here’s why..
Let’s assume the heights are: 1,2,3,4,5 & 6 feet
The way they are positioned is:
x x 6
1 x x
1 and 6 have to be at the above locations for the conditions to be fulfilled.
so, we need to fill in the x’s.
consider the guy with height 2 feet.
The only 2 possible locations for him are:
1. The x just above 1
2. The x just to the right of 1
Similarly, for the guy with height 3, there are 3 possible locations.
Height 4 and 5 also have 3 and 2 possible locations respectively.
So, no. of possible locations = 2 * 3 * 3 * 2 = 36.