Which of the following statement are correct?

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Number of words that can be formed with 6 only of the letters of the word “ CENTRIFUGAL” if each word must contain all the vowels is 3. 7!

There are 15 balls of which some are white and the rest black. If the number of ways in which the balls can be arranged in a row is maximum then the number of white balls must be equal to 7 or 8. Assume balls of the same colour to be alike.

There are 12 things, 4 alike of one kind, 5 alike and of another kind and the rest are all different the total number of combinations is 240.

Number of selections that can be made of 6 letters from the word “COMMITTEE” is 35.

answer is A, B, C, D.

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Detailed Solution

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$\Rightarrow^{7} C_{2} . 6! = 3.7. 6! = 3.7!$
(b) Number of ways $= \frac{15!}{r! (15 - r)!} =^{15} C_{r}$
$\underset{r}{\underset{⏟}{W W .... W}} \underset{15 - r}{\underset{⏟}{B B B ... B}}$
This is maximum if $r = 7 or 8$
(c ) Question Image

$\Rightarrow$ Total number of combinations $= 5. 6. 2 - 1 = 240 - 1 = 239$
(d) 2 alike +2 other alike +2other different =1
2 alike +2 other alike +2 different
$=^{3} C_{2} .^{4} C_{2} = 18$
2 alike + 4 different $=^{3} C_{1} .^{5} C_{1} = 15$
All 6 different $= \frac{1}{35}$