Dear Student, In word FATHERTotal number of alphabets=6Number of vowels=2Number of consonants=4iProbability both are vowels=2C26C2=16!2! 4!=2! 4!6 ×5 ×4!=115iiProbability one vowel and one not a vowel=2C1 ×4C1 6C2=2!1! × 1!×4!1! × 3!6!2! 4!=2 ×46 × 52=815 Regards

Ques no 42 pl

Dear Student,

In word FATHER Total number of alphabets = 6 Number of vowels = 2 Number of consonants = 4 (i) Probability (both are vowels) = \frac{{2_{C}}_{2}}{{6_{C}}_{2}} = \frac{1}{\frac{6!}{2! 4!}} = \frac{2! 4!}{6 \times 5 \times 4!} = \frac{1}{15} (ii) Probability (one vowel and one not a vowel) = \frac{{2_{C}}_{1} \times {4_{C}}_{1}}{{6_{C}}_{2}} = \frac{\frac{2!}{1! \times 1!} \times \frac{4!}{1! \times 3!}}{\frac{6!}{2! 4!}} = \frac{2 \times 4}{\frac{6 \times 5}{2}} = \frac{8}{15}

Regards

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