a/A class test consists of 4 Algebra questions,W ,X,Y and Z, and 3 Geometry questions,A,B,C and D.The teacher decides that the questions should be arranged in two sections.Algebra followed by Geometry,with questions in each section arranged in a random order Find the number of arrangement in which questions W and B are next to each other. Find the number of arrangements in which questions X and D are separated by more than four other subjects

Question

Reiny · Accepted Answer

W and B are next to each other:
let's put the there, then we have
? ? ? W B ? ? ?
3*2*1 W B 3*2*1
number of ways = 3*2*1*1*1*3*2*1 = 36

number of arrangements in which questions X and D are separated by more than four other subjects:
We already know that there are 36 cases where a X and D would be in specific places, (see first part, only the names would change)
case 1 , X is in the 1st position, so we could have
X ? ? ?|? ? D ? -----> 36 of those
X ? ? ?|? ? ? D -----> 36 of those
case 2:, the X is in the 2nd position
? X ? ?|? ? ? D -----> 36 of those
there are no other possibilities, so you
have 3(36) or 108 such cases.

Reiny · Answer

Three postings of the same question where you say "there are 3 geometry questions , A, B, C, and D." That's four! Clarify before I answer it

Raj · Answer

You are right.It was a typo

Reiny · Answer

So what is the correct version ????

Raj · Answer

A class test consists of 4 Algebra questions,W ,X,Y and Z, and 4 Geometry questions,A,B,C and D.The teacher decides that the questions should be arranged in two sections.Algebra followed by Geometry,with questions in each section arranged in a random order Find the number of arrangement in which questions W and B are next to each other. Find the number of arrangements in which questions X and D are separated by more than four other subjects.