Step 1

Introduction:

Combination:

Suppose there are n distinct items in a population. From these items, r distinct items are to be chosen, without any added constraints, in such a way that the order of choosing does not have any particular importance.

Then, the number of possible ways in which, the r distinct items can be chosen from the n distinct items in the population is “n combination r”, denoted as: \(\displaystyle_{n}{C}_{{r}}={n}!\text{/}{\left[{r}!{\left({n}-{r}\right)}!\right]}.\)

Step 2

Calculation:

There are 8 architects and 5 engineers. Thus, total number of individuals in the population is,

\(\displaystyle{n}={13}{\left(={8}+{5}\right)}.\)

Out of these individuals, \(r = 6\) members are to be chosen for a planning committee. Evidently, 6 distinct individuals must be chosen. There are no added constraints.

The number of ways in which the 6 members can be chosen from the 13 architects and engineers is:

\(\displaystyle_{13}{C}_{{6}}\)

\(\displaystyle={13}!\text{/}{\left[{6}!{\left({13}-{6}\right)}!\right]}\)

\(\displaystyle={13}!\text{/}{\left[{\left({6}!\right)}{\left({7}!\right)}\right]}\)

\(=1.716\)

Thus, the number of ways in which the 6 member-committee can be formed is 1.716

Introduction:

Combination:

Suppose there are n distinct items in a population. From these items, r distinct items are to be chosen, without any added constraints, in such a way that the order of choosing does not have any particular importance.

Then, the number of possible ways in which, the r distinct items can be chosen from the n distinct items in the population is “n combination r”, denoted as: \(\displaystyle_{n}{C}_{{r}}={n}!\text{/}{\left[{r}!{\left({n}-{r}\right)}!\right]}.\)

Step 2

Calculation:

There are 8 architects and 5 engineers. Thus, total number of individuals in the population is,

\(\displaystyle{n}={13}{\left(={8}+{5}\right)}.\)

Out of these individuals, \(r = 6\) members are to be chosen for a planning committee. Evidently, 6 distinct individuals must be chosen. There are no added constraints.

The number of ways in which the 6 members can be chosen from the 13 architects and engineers is:

\(\displaystyle_{13}{C}_{{6}}\)

\(\displaystyle={13}!\text{/}{\left[{6}!{\left({13}-{6}\right)}!\right]}\)

\(\displaystyle={13}!\text{/}{\left[{\left({6}!\right)}{\left({7}!\right)}\right]}\)

\(=1.716\)

Thus, the number of ways in which the 6 member-committee can be formed is 1.716