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Q:

There are 7 men and 10 women on a committee selection pool.A committee consisting of President,Vice-President, and Treasurer is to be formed.How many ways can exactly two men be on the committe ?

A) 1200	B) 1240
C) 1260	D) 1620

Answer & Explanation Answer: C) 1260

Explanation:

There are $7 C_{2}$ ways of selecting two men, and $10 C_{1}$ ways of selecting a woman.Since each position in the committee is different,arrange the three people in 3! ways.

So, $7 C_{2} * 10 C_{1} * 3! = 1260$

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Filed Under: Permutations and Combinations

Q:

A research team of 6 people is to be formed from 10 chemists,5 politicians, 8 economists and 15 biologists.How many teams have atleast 5 chemists?

A) 7350	B) 6400
C) 6379	D) 7266

Answer & Explanation Answer: D) 7266

Explanation:

$10 C_{5} * 28 C_{1} * 10 C_{6} = 7266$

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Filed Under: Permutations and Combinations

Q:

How many arrangements of the word TRIGONAL can be made if only two vowels and three consonants are used?

A) 6300	B) 3600
C) 6400	D) 7200

Answer & Explanation Answer: B) 3600

Explanation:

First we need to choose two vowels $3 C_{2}$ and then three consonants $5 C_{3}$ . Now that we have 5 letters required to make the word,arrange them in 5! ways.

So, $3 C_{2} * 5 C_{3} * 5! = 3600$

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Q:

If two painters can complete two rooms in two hours, how many painters would it take to do 18 rooms in 6 hours?

A) 2 painters	B) 6 painters
C) 4 painters	D) None

Answer & Explanation Answer: B) 6 painters

Explanation:

Two painters can complete two rooms in two hours.So 18 rooms can be painted in 6 hrs by 6 painters

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Filed Under: Problems on Numbers

Q:

A research team of 6 people is to be formed from 10 chemists,5 politicians, 8 economists and 15 biologists.How many teams have atleast 5 chemists?

A) 7350	B) 6400
C) 6379	D) 7266

Answer & Explanation Answer: D) 7266

Explanation:

10C5 x 28C1 x 10C6 = 7266

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Filed Under: Quantitative Aptitude - Arithmetic Ability

Q:

A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?

A) 715	B) 725
C) 419	D) 341

Answer & Explanation Answer: A) 715

Explanation:

If Jason is on th ecouncil,this reduces the selction pool to only 13 people,out of which we still need to select 4.

So, $13 C_{4}$ = 715

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Filed Under: Permutations and Combinations

Q:

If two painters can complete two rooms in two hours, how many painters would it take to do 18 rooms in 6 hours?

A) 2 painters	B) 6 painters
C) 4 painters	D) None

Answer & Explanation Answer: B) 6 painters

Explanation:

Two painters can complete two rooms in two hours.So 18 rooms can be painted in 6 hrs by 6 painters

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Filed Under: Problems on Numbers

Q:

From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?

A) 103336	B) 120000
C) 108336	D) 108333

Answer & Explanation Answer: C) 108336

Explanation:

The total possible cases would be a 5 card hand with no restrictions : $52 C_{5}$ 5

The unwanted cases are:

no queens(out of 48 non-queens cards we get 5) $48 C_{5}$

only 1 queen(out of 4 queens we get 1,and out of 48 non-queens we get 4) $4 C_{1} * 48 C_{4}$

Therefore, $52 C_{5} - (48 C_{5} + 4 C_{1} * 48 C_{4}) = 108336$

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Filed Under: Permutations and Combinations

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