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Home » We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

Solution:

It is known that,

=\frac{\mathrm{n} !}{\mathrm{r} !(\mathrm{n}-\mathrm{r}) !}

As per the question,

Case 1:

If both the persons A and B are selected =1 \times 1 \times ^{6} \mathrm{C}_{4}

=\frac{6 !}{4 !(6-4) !}=\frac{6 !}{4 ! 2 !}=15

Case 2:

If neither of the persons A nor B are selected ={ }^{6} C_{6}=1

If the person B is selected but the person A is not selected =1 \times ^{6} \mathrm{C}_{5}

=\frac{6 !}{5 !(6-4) !}=6

When we add the results of both persons A and B being selected, neither the person A or B being selected and the person B being selected but the person A not being selected,

We have,

15+1+6=22

i

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