Question

on No. 5 The number of ways of choosing (x+8) balls out of 36 balls is equal to choosing x balls out of 3 ball Fand the number of ways of choosing (n +5) balls out of 25 balls.

Answer 1

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Answer 2

The Correct question is: The number of ways of choosing (x+8) balls out of 36 balls is equal to choosing x balls out of 36 balls. Find the number of ways of choosing (x+5) balls out of 25 balls. ​

The Main Answer is: The required no. of ways of choosing is 177100.

Given: No. of ways of choosing (x+8) out of 36 balls = No. of ways of choosing x out of 36 balls.

To find: No. of ways of choosing (x+5) out of 25 balls

Solution:

The no. of ways of choosing 'r' things from a total of 'n' things is given by the formula:

                         $^{n} C_{r} = \frac{n!}{r! (n-r)!}$

∴ No. of ways of choosing (x+8) out of 36 balls = $^{36} C_{x+8}$

  No. of ways of choosing x out of 36 balls = $^{36} C_{x}$

According to the question-

                                    $^{36} C_{x+8} = ^{36} C_{x}$

This is only possible in 2 cases:

x+ 8 = x;            x+8 = 36 - x

Not Possible;   ∴ x+ 8 = 36-x

2x = 28 ⇒ x = 14

Now,

No. of ways of choosing x+5 out of 25 balls = $^{25} C_{14 + 5}$ = $^{25} C_{19}$

$^{25} C_{19} = \frac{25!}{14!6!}$ = 25×24×23×22×21×20×19! = 177100

                           19! ×6×5×4×3×2×1

Therefore, no. of ways of choosing x+5 out of 25 balls = 177100

For a similar question on Combinations, refer to:

https://brainly.in/question/26851266

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