The student should answer 10 questions out of 13 on condition that he should answer 4 questions at least from first 5 questions . how many ways can he answer?
in advance

answer is 196

Step-by-step explanation:  If the student answers 4 questions from the first five questions he can choose 6 questions from the remaining 8 questions. Therefore number of combinations will be

5C4×8C6=140

If the student answers 5 questions from the first five questions he can choose 5 questions from the remaining 8 questions. Which will be

5C5×8C5=56

Therefore total number of choices= 140+56=196

check the picture below.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions