Given below are two statements
Statement I : A committee of 4 can be made out of 5 men and 3 women containing at least one woman in 65 ways.
Statement II : The number of words which can be formed using letters of the word ARRANGE' so that vowels always occupy even place is 36.
In light of the above statements, choose the correct answer from the options given below
Solution
Now we have 5 men and 3 women
committee of 4 to be made such that it has at least 1 woman
Case 1 :
1W and 3M
We get $$^5C_3\times\ ^3C_{1\ }=\ 30$$
Case 2 : 2W 2M
$$^5C_2\times\ ^3C_{2\ }=\ 30$$
Case 3 : 3W 1 M
$$^5C_1\times\ ^3C_{3\ }=\ 5$$
So total cases = 65.
so 1 is true
Now
ARRANGE
If vowels to be at even position :
we get cases as $$\frac{3!}{2!}\times\ \frac{4!}{2!}$$ = 36
So statement 2 is true
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