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Permutations and Combinations

Short Answer Type

221.

How many 3-digit numbers are there with no digit repeat?

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222.

How many 3-digit odd numbers are there?

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223.

If $2 times straight P presuperscript 5 subscript 3 space equals space straight P presuperscript straight n subscript 4 comma$ find n.

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224.

If $straight P presuperscript 10 subscript straight r space equals space 5040 comma$ find value of r.

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225. In how many ways can three different rings be worn in tour lingers with at most one ring in a finger ?

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226. Seven athletes are participating in a race. In how many ways can the three prizes be won?

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227. From amongst 16 teachers in a school, one principal and one vice-principal is to be appointed? In how many ways can this be done?

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228. How many words can be formed by using the letters of word ‘TRIANGLE’ when the vowels are to be all together?

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229. How many words can be made using letters of the word ‘DELHI’. How many of these end with I?

Solution not provided.

Ans. (a) 120 (b) 24

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230. In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

[Hint : 6! x 5!]

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