
In how many ways can a person go from point to point if he can travel only to the right or upward along the lines (Grid Problem)?

Answer
491.4k+ views
Hint: In this type of problem we need to find the ways from the point to point in the given figure by using the method of grid problem.
Here we have to use the formula for combination to solve this question.
Let us do some simplification, we get the required answer.
Formula used:
Complete step-by-step answer:
In the given figure below
This is slightly different from the usual approach, to reach to we have to go steps right and steps upwards in any order.
The number of possible arrangements of and will give the number of different paths.
The number of arrangements is given by
Here and by using the formula we get,
Now let us expand the above expression by using the formula of combination
On cancellation of terms in the numerator and denominator we get,
We can have,
Now we are multiplying the remaining terms
(As the and are identical)
Hence, we get the required number of ways are which is in the option of
Hence, we get the number of ways a person can go from point to point if he can travel only to the right or upwards along the line.
Note: In general, permutation can be defined as the act of arranging all the members of a group in an order or sequence. We can also say that if the group is already arranged, then rearranging of the members is known as the procedure of permuting.
Combination can be defined as the technique of selecting things from a collection in such a manner that the order of selection does not matter. It is generally used where the order of data does not matter.
Here we have to use the formula for combination to solve this question.
Let us do some simplification, we get the required answer.
Formula used:
Complete step-by-step answer:
In the given figure below

This is slightly different from the usual approach, to reach
The number of possible arrangements of
The number of arrangements is given by
Here
Now let us expand the above expression by using the formula of combination
On cancellation of terms in the numerator and denominator we get,
We can have,
Now we are multiplying the remaining terms
(As the
Hence, we get the required number of ways are
Hence, we get the number of ways a person can go from point
Note: In general, permutation can be defined as the act of arranging all the members of a group in an order or sequence. We can also say that if the group is already arranged, then rearranging of the members is known as the procedure of permuting.
Combination can be defined as the technique of selecting things from a collection in such a manner that the order of selection does not matter. It is generally used where the order of data does not matter.
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