lashawnnb2397 lashawnnb2397

08-09-2018
Mathematics

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How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appears consecutively?

Respuesta :

zrh2sfo zrh2sfo

08-09-2018

Take an ordering of the consonants (there are 21! such orderings), for example:

bcdfghjklmnpqrstvwxyz

Enumerate the 22 "slots" between these consonants:

_b_c_d_f_g_h_j_k_l_m_n_p_q_r_s_t_v_w_x_y_z_

We can choose (respecting order) ₂₂P₅ lists of five slots to put the vowels aeiou in order.

The answer is therefore ₂₂P₅ ₓ 21!

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