If C n + 7 35 = C 4 n - 2 35 then find the value of n .

Given: C n + 7 35 = C 4 n - 2 35 We have to find the value of n . We know, one of the property of combination is: If C r n = C t n , then, i r = t or ( ii ) r + t = n Applying property ( i ) we get, ⇒ n + 7 = 4 n - 2 ⇒ 3 n = 9 ⇒ n = 3 Applying property ( ii ) we get, ⇒ n + 7 + 4 n - 2 = 35 ⇒ 5 n = 30 ⇒ n = 6 Therefore, the value of n is either 3 or 6 .

E M B I B E

Senior Secondary School Mathematics FOR CLASS 11>Chapter 9 - Combinations>EXERCISE 9C>Q 3

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The English alphabet has $21$ consonants and $5$ vowels. How many words with two different consonants and three different vowels can be formed from the alphabet?

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Important Questions on Combinations

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Senior Secondary School Mathematics FOR CLASS 11>Chapter 9 - Combinations>EXERCISE 9C>Q 4

In how many ways can

4

girls and

3

boys be seated in a row so that no two boys are together?

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Senior Secondary School Mathematics FOR CLASS 11>Chapter 9 - Combinations>EXERCISE 9C>Q 5

How many words, with or without meaning, can be formed from the letters of the word, 'MONDAY', assuming that no letter is repeated, if $4$ letters are used at a time?

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Senior Secondary School Mathematics FOR CLASS 11>Chapter 9 - Combinations>EXERCISE 9C>Q 5

How many words, with or without meaning, can be formed from the letters of the word, 'MONDAY', assuming that no letter is repeated, if

all letters are used at a time?

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11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 9 - Combinations>EXERCISE 9C>Q 5

How many words, with or without meaning, can be formed from the letters of the word, 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?

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Senior Secondary School Mathematics FOR CLASS 11>Chapter 9 - Combinations>EXERCISE 9D>Q 1

If