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Standard XII

Mathematics

Combination

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Question

There are $13$ letters of $8$ different sorts $I, I, I, S, S, T, T, L, L, A, O, N, D$ . In finding groups of $4$ , how many permutations can be made if following are the possibilities to be considered? If all the four are distinct

1680

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1201

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1600

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1425

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Solution

The correct option is A $1680$
Given that there are $13$ letters totally out of which $8$ are district.
We need to choose $4$ from these $8$ district letters.
$\Rightarrow$ Total permutations $=^{8} P_{4} = 8 \times 7 \times 6 \times 5 = 1680$
Hence, the answer is $1680.$

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Similar questions

Q. There are

13

letters of

8

different sorts

I, I, I, S, S, T, T, L, L, A, O, N, D

. In finding groups of

4

, how many permutations can be made if following are the possibilities to be considered? If

2

are alike of one kind and

2

are alike of other kind.

In how many ways can the letters of the word PERMUTATIONS be arranged if the

(i) words start with P and end with S?

(ii) vowels are all together?

(iii) there are always 4 letters between P and S?

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and end with

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(i i)

Vowels are all together

(i i i)

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letters between

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and

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(i) words start with P and end with S, (ii) vowels are all together,

(ii) there are always 4 letters between P and S?

Q. In how many ways can a letters of the word

P E R M U T A T I O N S

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There are 13 letters of 8 different sorts I,I,I,S,S,T,T,L,L,A,O,N,D. In finding groups of 4, how many permutations can be made if following are the possibilities to be considered? If all the four are distinct

The correct option is A 1680Given that there are 13 letters totally out of which 8 are district. We need to choose 4 from these 8 district letters.⇒ Total permutations =8P4=8×7×6×5=1680Hence, the answer is 1680.

There are $13$ letters of $8$ different sorts $I, I, I, S, S, T, T, L, L, A, O, N, D$ . In finding groups of $4$ , how many permutations can be made if following are the possibilities to be considered? If all the four are distinct

The correct option is A $1680$
Given that there are $13$ letters totally out of which $8$ are district.
We need to choose $4$ from these $8$ district letters.
$\Rightarrow$ Total permutations $=^{8} P_{4} = 8 \times 7 \times 6 \times 5 = 1680$
Hence, the answer is $1680.$