Question

in how many ways three leads be selected out of 5 males and 4 females if atleast One female has to be selected ​

Answer 1

SOLUTION :

TO DETERMINE

The number of ways three leads be selected out of 5 males and 4 females if atleast One female has to be selected

EVALUATION

Let F denotes Female and M denotes the Male

Here total number of males = 5 & total number of females = 4

Now 3 leads are to be selected such that atleast One female has to be selected

This can be performed as below

Case : I 3 leads are female

In this case the number of ways 3 female leads can be selected from 4 females

$= \sf{ \large{ {}^{4} C_3}}$

$= \sf{}4$

So In this case total number of ways = 4

Case : II 2 leads are female & 1 is male

In this case the number of ways 2 female leads and 1 male leads can be selected from 5 males and 4 females

$= \sf{ \large{ {}^{4} C_2} \times \large{ {}^{5} C_1} }$

$= \sf{}6 \times 5$

$\sf{} = 30$

So In this case total number of ways = 30

Case : III 1 leads are female & 2 is male

In this case the number of ways 1 female leads and 2 male leads can be selected from 5 males and 4 females

$= \sf{ \large{ {}^{4} C_1} \times \large{ {}^{5} C_2} }$

$= \sf{ }4 \times 10$

$\sf{} = 40$

So In this case total number of ways = 40

Hence the total number of ways

$\sf{} = 4 + 30 + 40$

$= \sf{}74$

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